Combinatorial Stochastic Processes

Preliminaries.- Bell polynomials, composite structures and Gibbs partitions.- Exchangeable random partitions.- Sequential constructions of random partitions.- Poisson constructions of random partitions.- Coagulation and fragmentation processes.- Random walks and random forests.- The Brownian forest.- Brownian local times, branching and Bessel processes.- Brownian bridge asymptotics for random mappings.- Random forests and the additive coalescent.

[1]  E. N.,et al.  The Calculus of Finite Differences , 1934, Nature.

[2]  A. Huber,et al.  Theorie und Anwendung der Laplace-Transformation , 1939 .

[3]  P. Levy Sur certains processus stochastiques homogènes , 1940 .

[4]  I. M. H. Etherington,et al.  Some problems of non-associative combinations (2) , 1940 .

[5]  W. Feller,et al.  The fundamental limit theorems in probability , 1945 .

[6]  R. Otter The Multiplicative Process , 1949 .

[7]  Johannes Henricus Bernardus Kemperman The general one-dimensional random walk with absorbing barriers : with applications to sequential analysis , 1950 .

[8]  W. Feller The Asymptotic Distribution of the Range of Sums of Independent Random Variables , 1951 .

[9]  D. Kendall Some Problems in the Theory of Queues , 1951 .

[10]  T. E. Harris First passage and recurrence distributions , 1952 .

[11]  The Number of Cycles Associated with the Elements of a Permutation Group , 1953 .

[12]  E. Lukács Applications of Faá Di Bruno's Formula in Mathematical Statistics , 1955 .

[13]  W. Hayman A Generalisation of Stirling's Formula. , 1956 .

[14]  David G. Kendall,et al.  Some Problems in the Theory of Dams , 1957 .

[15]  John Riordan,et al.  Introduction to Combinatorial Analysis , 1959 .

[16]  G. N. Raney Functional composition patterns and power series reversion , 1960 .

[17]  A. F. Filippov On the Distribution of the Sizes of Particles which Undergo Splitting , 1961 .

[18]  Lajos Takács,et al.  A Generalization of the Ballot Problem and its Application in the Theory of Queues , 1962 .

[19]  John Lamperti,et al.  An Invariance Principle in Renewal Theory , 1962 .

[20]  B. Harris The Passage Problem for a Stationary Markov Chain , 1962 .

[21]  O. Wing Enumeration of Trees , 1963 .

[22]  H. McKean,et al.  Excursions of a non-singular diffusion , 1963 .

[23]  S. Karlin,et al.  Conditioned Limit Theorems , 1963 .

[24]  F. Knight,et al.  Random walks and a sojourn density process of Brownian motion , 1963 .

[25]  Zero-Free Intervals of Semi-Stable Markov Processes. , 1964 .

[26]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[27]  A Formal Solution of Σ∞ i=1 AieBix = X , 1964, Canadian Journal of Mathematics.

[28]  P. Whittle Statistical processes of aggregation and polymerization , 1965, Mathematical Proceedings of the Cambridge Philosophical Society.

[29]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[30]  P. Whittle,et al.  The equilibrium statistics of a clustering process in the uncondensed phase , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[31]  J. McCloskey,et al.  A model for the distribution of individuals by species in an environment , 1965 .

[32]  W. G. Brown,et al.  Historical Note on a Recurrent Combinatorial Problem , 1965 .

[33]  L. A. Shepp,et al.  Ordered cycle lengths in a random permutation , 1966 .

[34]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[35]  S. Karlin Central Limit Theorems for Certain Infinite Urn Schemes , 1967 .

[36]  L. Harper Stirling Behavior is Asymptotically Normal , 1967 .

[37]  John Lamperti,et al.  The Limit of a Sequence of Branching Processes , 1967 .

[38]  J. Lamperti Limiting distributions for branching processes , 1967 .

[39]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. 1 , 1967 .

[40]  Diffusion Processes and their Sample Paths. , 1968 .

[41]  J. Kingman Random Processes , 2019, Nature.

[42]  B. Brown Moments of a Stopping Rule Related to the Central Limit Theorem , 1969 .

[43]  S. Molchanov,et al.  Symmetric Stable Processes as Traces of Degenerate Diffusion Processes , 1969 .

[44]  David Williams,et al.  Decomposing the Brownian path , 1970 .

[45]  W. J. Hall On Wald's equations in continuous time , 1970, Journal of Applied Probability.

[46]  Shinzo Watanabe,et al.  Branching Processes with Immigration and Related Limit Theorems , 1971 .

[47]  I. Ibragimov,et al.  Independent and stationary sequences of random variables , 1971 .

[48]  A. V. Boyd,et al.  Formal power series and the total progeny in a branching process , 1971 .

[49]  W. Ewens The sampling theory of selectively neutral alleles. , 1972, Theoretical population biology.

[50]  Convergence of critical Galton-Watson branching processes , 1972 .

[51]  J. Neveu,et al.  Martingales à temps discret , 1973 .

[52]  D. Blackwell,et al.  Ferguson Distributions Via Polya Urn Schemes , 1973 .

[53]  R. M. Korwar,et al.  Contributions to the Theory of Dirichlet Processes , 1973 .

[54]  Alan G. Konheim,et al.  A note on growing binary trees , 1973, Discret. Math..

[55]  Edward A. Bender,et al.  Central and Local Limit Theorems Applied to Asymptotic Enumeration , 1973, J. Comb. Theory A.

[56]  O. Kallenberg Canonical representations and convergence criteria for processes with interchangeable increments , 1973 .

[57]  Gian-Carlo Rota,et al.  On the foundations of combinatorial theory. VIII. Finite operator calculus , 1973 .

[58]  T. Ferguson A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[59]  D. Freedman Another Note on the Borel-Cantelli Lemma and the Strong Law, with the Poisson Approximation as a By-product , 1973 .

[60]  Shinzo Watanabe,et al.  Bessel diffusions as a one-parameter family of diffusion processes , 1973 .

[61]  Bradford R. Cain,et al.  Approximating Countable Markov Chains , 1974 .

[62]  C. Antoniak Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[63]  D. Iglehart Functional Central Limit Theorems for Random Walks Conditioned to Stay Positive , 1974 .

[64]  Harold J. Kushner,et al.  On the Weak Convergence of Interpolated Markov Chains to a Diffusion , 1974 .

[65]  Jim Pitman ONE-DIMENSIONAL BROWNIAN MOTION AND THE THREE-DIMENSIONAL BESSEL PROCESS , 1974 .

[66]  J. Pitman Uniform rates of convergence for Markov chain transition probabilities , 1974 .

[67]  E. Bender Asymptotic Methods in Enumeration , 1974 .

[68]  David M. Williams Path Decomposition and Continuity of Local Time for One‐Dimensional Diffusions, I , 1974 .

[69]  Reuel Shinnar,et al.  The Extent of Correlations in a Stochastic Coalescence Process , 1974 .

[70]  J. G. Wendel Left-Continuous Random Walk and the Lagrange Expansion , 1975 .

[71]  C. Cannings The latent roots of certain Markov chains arising in genetics: A new approach, II. Further haploid models , 1975, Advances in Applied Probability.

[72]  Ihrer Grenzgebiete,et al.  Ergebnisse der Mathematik und ihrer Grenzgebiete , 1975, Sums of Independent Random Variables.

[73]  On Refining Partitions , 1975 .

[74]  Erwin Bolthausen,et al.  On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive , 1976 .

[75]  D. P. Kennedy,et al.  The distribution of the maximum Brownian excursion , 1976, Journal of Applied Probability.

[76]  Kai Lai Chung,et al.  Excursions in Brownian motion , 1976 .

[77]  G. A. Watterson The stationary distribution of the infinitely-many neutral alleles diffusion model , 1976 .

[78]  W. D. Kaigh An Invariance Principle for Random Walk Conditioned by a Late Return to Zero , 1976 .

[79]  E. Rodney Canfield,et al.  Central and Local Limit Theorems for the Coefficients of Polynomials of Binomial Type , 1977, J. Comb. Theory, Ser. A.

[80]  Donald L. Iglehart,et al.  Weak Convergence to Brownian Meander and Brownian Excursion , 1977 .

[81]  Steinar Engen Stochastic abundance models, with emphasis on biological communities and species diversity , 1978 .

[82]  A. A Lushnikov,et al.  Coagulation in finite systems , 1978 .

[83]  A. Rouault,et al.  Lois de Zipf et sources markoviennes , 1978 .

[84]  Special Functions, Probability Semigroups, and Hamiltonian Flows , 1978 .

[85]  J. Kingman The Representation of Partition Structures , 1978 .

[86]  Yu. L. Pavlov The Asymptotic Distribution of Maximum Tree Size in a Random Forest , 1978 .

[87]  J. Kingman Random partitions in population genetics , 1978, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[88]  J. Moon,et al.  On the Altitude of Nodes in Random Trees , 1978, Canadian Journal of Mathematics.

[89]  L. Rogers,et al.  Diffusions, Markov processes, and martingales , 1979 .

[90]  W. Vervaat,et al.  A Relation between Brownian Bridge and Brownian Excursion , 1979 .

[91]  Y. D. Burtin On a simple formula for random mappings and its applications , 1980, Journal of Applied Probability.

[92]  T. Rolski On random discrete distributions , 1980 .

[93]  Jim Pitman,et al.  Fluctuation identities for Levy processes and splitting at the maximum , 1980 .

[94]  C. J-F,et al.  THE COALESCENT , 1980 .

[95]  J. Kingman,et al.  Mathematics of genetic diversity , 1982 .

[96]  B. Derrida Random-energy model: An exactly solvable model of disordered systems , 1981 .

[97]  Endre Csáki,et al.  Excursion and meander in random walk , 1981 .

[98]  F. Knight Essentials of Brownian Motion and Diffusion , 1981 .

[99]  Gilbert Labelle,et al.  Une nouvelle démonstration combinatoire des formules d'inversion de Lagrange , 1981 .

[100]  A. Joyal Une théorie combinatoire des séries formelles , 1981 .

[101]  Lars Holst On Numbers Related to Partitions of Unlike Objects and Occupancy Problems , 1981, Eur. J. Comb..

[102]  C. Morris Natural Exponential Families with Quadratic Variance Functions , 1982 .

[103]  J. Pitman,et al.  A decomposition of Bessel Bridges , 1982 .

[104]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[105]  R. Blumenthal Weak Convergence to Brownian Excursion , 1983 .

[106]  George Szekeres,et al.  Distribution of labelled trees by diameter , 1983 .

[107]  L. Rogers Brownian local times and branching processes , 1984 .

[108]  Paavo Salminen Brownian Excursions Revisited , 1984 .

[109]  J. Imhof,et al.  Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications , 1984, Journal of Applied Probability.

[110]  S. Tavaré,et al.  Line-of-descent and genealogical processes, and their applications in population genetics models. , 1984, Theoretical population biology.

[111]  B. Pittel On growing random binary trees , 1984 .

[112]  T. Jeulin Ray-Knight’s Theorem on Brownian Local Times and Tanaka’s Formula , 1984 .

[113]  B. Bollobás The evolution of random graphs , 1984 .

[114]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[115]  G. A. Watterson Lines of descent and the coalescent , 1984 .

[116]  J. van Pelt,et al.  Growth models (including terminal and segmental branching) for topological binary trees. , 1985, Bulletin of mathematical biology.

[117]  M. Schreckenberg,et al.  Exact solutions for random coagulation processes , 1985 .

[118]  T. Jeulin Application de la theorie du grossissement a l'etude des temps locaux Browniens , 1985 .

[119]  D. Aldous Exchangeability and related topics , 1985 .

[120]  On the Duration of the Longest Excursion , 1986 .

[121]  J. Neveu Erasing a branching tree , 1986 .

[122]  J. Neveu,et al.  Arbres et processus de Galton-Watson , 1986 .

[123]  J. Gall Une approche elementaipe des theoremes de decomposition de Williams , 1986 .

[124]  P. Donnelly,et al.  The ages of alleles and a coalescent , 1986, Advances in Applied Probability.

[125]  J. van Pelt,et al.  Topological properties of binary trees grown with order-dependent branching probabilities. , 1986, Bulletin of mathematical biology.

[126]  H. Kesten Subdiffusive behavior of random walk on a random cluster , 1986 .

[127]  Operational derivation of some Brownian motion results , 1986 .

[128]  M. Nordborg,et al.  Coalescent Theory , 2019, Handbook of Statistical Genomics.

[129]  F. Hoppe Size-biased filtering of Poisson–Dirichlet samples with an application to partition structures in genetics , 1986, Journal of Applied Probability.

[130]  Ph. Biane Relations entre pont et excursion du mouvement Brownien réel , 1986 .

[131]  Excursions browniennes et carrés de processus de Bessel , 1986 .

[132]  Peter Whittle,et al.  Systems in stochastic equilibrium , 1986 .

[133]  L. Rogers,et al.  Self-avoiding random walk: A Brownian motion model with local time drift , 1987 .

[134]  Kevin J. Compton,et al.  Some methods for computing component distribution probabilities in relational structures , 1987, Discret. Math..

[135]  S. Tavaré The birth process with immigration, and the genealogical structure of large populations , 1987, Journal of mathematical biology.

[136]  M. Yor,et al.  Un processus qui ressemble au pont brownien , 1987 .

[137]  Simon Tavaré,et al.  Cycles, permutations and the structure of the yule process with immigration , 1987 .

[138]  M. Yor,et al.  Valeurs principales associées aux temps locaux browniens , 1987 .

[139]  A. J. Stam Some stochastic processes in a random permutation , 1988 .

[140]  Lajos Takács Queues, random graphs and branching processes , 1988 .

[141]  M. Yor,et al.  Sur la loi des temps locaux browniens pris en un temps exponentiel , 1988 .

[142]  Quelques précisions sur le méandre brownien , 1988 .

[143]  O. Kallenberg One dimensional uniqueness and convergence criteria for exchangeable processes , 1988 .

[144]  A. J. Stam,et al.  POLYNOMIALS OF BINOMIAL TYPE AND COMPOUND POISSON PROCESSES , 1988 .

[145]  Jim Pitman,et al.  The branching process in a Brownian excursion , 1989 .

[146]  Philippe Flajolet,et al.  Random Mapping Statistics , 1990, EUROCRYPT.

[147]  J. -. Gall,et al.  Marches aleatoires, mouvement brownien et processus de branchement , 1989 .

[148]  Charles M. Goldie,et al.  Records, permutations and greatest convex minorants , 1989, Mathematical Proceedings of the Cambridge Philosophical Society.

[149]  Andrei Z. Broder,et al.  Generating random spanning trees , 1989, 30th Annual Symposium on Foundations of Computer Science.

[150]  J. Hansen FOR THE EWENS SAMPLING FORMULA , 1990 .

[151]  David Aldous,et al.  A Random Tree Model Associated with Random Graphs , 1990, Random Struct. Algorithms.

[152]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[153]  Lajos Takács,et al.  Counting forests , 1990, Discret. Math..

[154]  R. Durrett Probability: Theory and Examples , 1993 .

[155]  David Aldous,et al.  The Continuum Random Tree III , 1991 .

[156]  Mekjian Cluster distributions in physics and genetic diversity. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[157]  D. Aldous Stochastic Analysis: The Continuum random tree II: an overview , 1991 .

[158]  J. L. Gall,et al.  Brownian excursions, trees and measure-valued branching processes , 1991 .

[159]  Harry Kesten,et al.  On weighted heights of random trees , 1991 .

[160]  P. Hilton,et al.  Catalan Numbers, Their Generalization, and Their Uses , 1991 .

[161]  P. Donnelly,et al.  Consistent ordered sampling distributions : characterization and convergence , 1991 .

[162]  Absolute continuity results for superprocesses with some applications , 1991 .

[163]  P. Protter,et al.  Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations , 1991 .

[164]  David Aldous,et al.  The number of extreme points in the convex hull of a random sample , 1991 .

[165]  J. V. Pulé,et al.  Polymers and random graphs , 1991 .

[166]  Lee,et al.  Models of fragmentation and partitioning phenomena based on the symmetric group Sn and combinational analysis. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[167]  Lee,et al.  Canonical studies of the cluster distribution, dynamical evolution, and critical temperature in nuclear multifragmentation processes. , 1992, Physical review. C, Nuclear physics.

[168]  M. Marcus,et al.  Sample Path Properties of the Local Times of Strongly Symmetric Markov Processes Via Gaussian Processes , 1992 .

[169]  Ljuben R. Mutafchiev,et al.  Local Limit Theorems for Sums of Power Series Distributed Random Variables and for the Number of Components in Labelled Relational Structures , 1992, Random Struct. Algorithms.

[170]  Renormalization and Limit Theorems for Self-Intersections of Superprocesses , 1992 .

[171]  G. Pflug,et al.  The asymptotic contour process of a binary tree is a Brownian excursion , 1992 .

[172]  Un arbre aléatoire infini associé à l'excursion brownienne , 1992 .

[173]  B. Harris,et al.  The early history of the theory of random mappings , 1992, Advances in Applied Probability.

[174]  W. Sudderth,et al.  Polya Trees and Random Distributions , 1992 .

[175]  J. Bertoin An Extension of Pitman's Theorem for Spectrally Positive Levy Processes , 1992 .

[176]  J. Pitman,et al.  Size-biased sampling of Poisson point processes and excursions , 1992 .

[177]  Jim Pitman,et al.  Arcsine Laws and Interval Partitions Derived from a Stable Subordinator , 1992 .

[178]  Mihael Perman,et al.  Order statistics for jumps of normalised subordinators , 1993 .

[179]  René Schott,et al.  Algebraic Structures and Operator Calculus , 1993 .

[180]  Moshe Sidi,et al.  Growing binary trees in a random environment , 1993, IEEE Trans. Inf. Theory.

[181]  Svante Janson,et al.  The Birth of the Giant Component , 1993, Random Struct. Algorithms.

[182]  J. Gall The uniform random tree in a Brownian excursion , 1993 .

[183]  László Lovász,et al.  Combinatorial problems and exercises (2. ed.) , 1993 .

[184]  Walter J. Gutjahr,et al.  Expectation Transfer between Branching Processes and Random Trees , 1993, Random Struct. Algorithms.

[185]  Jim Pitman,et al.  Markovian Bridges: Construction, Palm Interpretation, and Splicing , 1993 .

[186]  Philippe Biane Some Comments on the Paper "Brownian Bridge Asymptotics for Random Mappings" , 1994, Random Struct. Algorithms.

[187]  P. Carmona,et al.  Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion , 1994 .

[188]  Jim Pitman,et al.  Path transformations connecting Brownian bridge, excursion and meander , 1994 .

[189]  Jennie C. Hansen,et al.  Order Statistics for Decomposable Combinatorial Structures , 1994, Random Struct. Algorithms.

[190]  Nuclear fragmentation and its parallels. , 1993, Physical review. C, Nuclear physics.

[191]  Sergei V. Kerov,et al.  The Boundary of Young Lattice and Random Young Tableaux , 1994, Formal Power Series and Algebraic Combinatorics.

[192]  William M. Y. Goh,et al.  Random Set Partitions , 1994, SIAM J. Discret. Math..

[193]  Jim Pitman,et al.  Brownian bridge asymptotics for random mappings , 1992, Advances in Applied Probability.

[194]  David Aldous RECURSIVE SELF-SIMILARITY FOR RANDOM TREES, RANDOM TRIANGULATIONS AND BROWNIAN EXCURSION , 1994 .

[195]  Some aspects of Brownian motion. Part I: Some special functionals , 1994 .

[196]  F. Steutel,et al.  Infinite divisibility and the waiting-time paradox , 1994 .

[197]  Random Brownian Scaling and Some Absolute Continuity Relationships , 1995 .

[198]  Peter W. Shor,et al.  A New Proof of Cayley's Formula for Counting Labeled Trees , 1995, J. Comb. Theory, Ser. A.

[199]  R. Berk,et al.  Continuous Univariate Distributions, Volume 2 , 1995 .

[200]  Peter Littelmann,et al.  Paths and root operators in representation theory , 1995 .

[201]  The limit distributions of the maximum size of a tree in a random forest , 1995 .

[202]  J. Pitman Exchangeable and partially exchangeable random partitions , 1995 .

[203]  Les théorèmes de ray-knight et la mesure d'ti:ô pour le mouvement brownien sur le tore R/Z , 1995 .

[204]  The asymptotics of interlacing sequences and the growth of continual young diagrams , 1996 .

[205]  J. Pitman Some developments of the Blackwell-MacQueen urn scheme , 1996 .

[206]  An excursion approach to Ray-Knight theorems for perturbed Brownian motion , 1996 .

[207]  A. Odlyzko Asymptotic enumeration methods , 1996 .

[208]  Jim Pitman,et al.  Cyclically stationary Brownian local time processes , 1996 .

[209]  J. Pitman,et al.  Random Discrete Distributions Derived from Self-Similar Random Sets , 1996 .

[210]  P. R. Nelson Continuous Univariate Distributions Volume 2 , 1996 .

[211]  H. McKean,et al.  Diffusion processes and their sample paths , 1996 .

[212]  J. Pitman,et al.  Decomposition at the maximum for excursions and bridges of one-dimensional diffusions , 1996 .

[213]  J. Wellner,et al.  On the distribution of Brownian areas , 1996 .

[214]  J. Geiger Size-biased and conditioned random splitting trees , 1996 .

[215]  J. Pitman Random discrete distributions invariant under size-biased permutation , 1996, Advances in Applied Probability.

[216]  On the Markov property of local time for Markov processes on graphs , 1996 .

[217]  Jim Pitman,et al.  Probabilistic Bounds on the Coefficients of Polynomials with Only Real Zeros , 1997, J. Comb. Theory, Ser. A.

[218]  Jim Pitman,et al.  On the relative lengths of excursions derived from a stable subordinator , 1997 .

[219]  O. Kallenberg Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[220]  J. Pitman Some Probabilistic Aspects of Set Partitions , 1997 .

[221]  Bernard Derrida,et al.  From random walks to spin glasses , 1997 .

[222]  M. Perman,et al.  Perturbed Brownian motions , 1997 .

[223]  A. Mekjian,et al.  Disordered systems, power laws and random processes , 1997 .

[224]  Gilbert Labelle,et al.  Combinatorial species and tree-like structures , 1997, Encyclopedia of mathematics and its applications.

[225]  Cori Robert Combinatorics on words: Words and Trees , 1997 .

[226]  J. Pitman,et al.  The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator , 1997 .

[227]  J. Pitman Coalescent Random Forests , 1997 .

[228]  On the lengths of excursions of some Markov processes , 1997 .

[229]  G. Kersting,et al.  Depth—First Search of Random Trees, and Poisson Point Processes , 1997 .

[230]  Grigori Olshanski,et al.  The boundary of the Young graph with Jack edge multiplicities , 1997 .

[231]  Alexander Gnedin,et al.  The representation of composition structures , 1997 .

[232]  David Aldous,et al.  Brownian excursions, critical random graphs and the multiplicative coalescent , 1997 .

[233]  Jim Pitman,et al.  Enumerations of trees and forests related to branching processes and random walks , 1997, Microsurveys in Discrete Probability.

[234]  L. Chaumont Excursion normalisée, méandre et pont pour les processus de Lévy stables , 1997 .

[235]  Jim Pitman,et al.  Partition structures derived from Brownian motion and stable subordinators , 1997 .

[236]  Jim Pitman,et al.  The standard additive coalescent , 1998 .

[237]  CoalescenceDavid J. Aldous Stochastic Coalescence , 1998 .

[238]  Y. Jan,et al.  Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses , 1998 .

[239]  D. Dufresne Algebraic Properties of Beta and Gamma Distributions, and Applications , 1998 .

[240]  M. Yor,et al.  The Brownian Burglar: conditioning Brownian motion by its local time process , 1998 .

[241]  David Aldous Brownian Excursion Conditioned on Its Local Time , 1998 .

[242]  S. Feng,et al.  Large deviation principles for some random combinatorial structures in population genetics and Brownian motion , 1998 .

[243]  Processesby Jim Pitman Random Brownian Scaling Identities and Splicing of Bessel Processes , 1997 .

[244]  A. Gnedin On convergence and extensions of size-biased permutations , 1998 .

[245]  J. L. Gall,et al.  Branching processes in Lévy processes: the exploration process , 1998 .

[246]  Le théorème de ray-knight à temps fixe , 1998 .

[247]  Jim Pitman,et al.  Construction of markovian coalescents , 1998 .

[248]  Symmetry Properties of Binary Branching Trees , 1998 .

[249]  Tomasz Luczak Random trees and random graphs , 1998, Random Struct. Algorithms.

[250]  Tomasz Łuczak,et al.  Random trees and random graphs , 1998 .

[251]  Marc Yor,et al.  Beta-gamma random variables and intertwining relations between certain Markov processes , 1998 .

[252]  Amir Dembo,et al.  Large deviations for integer partitions , 1998 .

[253]  David Aldous,et al.  The Entrance Boundary of the Multiplicative Coalescent , 1998 .

[254]  Jim Pitman,et al.  Tree-valued Markov chains derived from Galton-Watson processes , 1998 .

[255]  F. Guerra,et al.  Ju l 1 99 8 General properties of overlap probability distributions in disordered spin systems , 1998 .

[256]  Collision Local Times, Historical Stochastic Calculus, and Competing Species , 1998 .

[257]  E. Bolthausen,et al.  On Ruelle's Probability Cascades and an Abstract Cavity Method , 1998 .

[258]  Jim Pitman,et al.  A family of random trees with random edge lengths , 1999, Random Struct. Algorithms.

[259]  P. Ressel,et al.  Random Partitions by Semigroup Methods , 1999 .

[260]  Johannes Lenhard,et al.  Six Ways of Looking at Burtin's Lemma , 1999 .

[261]  De Chavez,et al.  Constructions of a Brownian path with a given minimum , 2016 .

[262]  Jim Pitman,et al.  The Law of the Maximum of a Bessel Bridge , 1999 .

[263]  On the laws of homogeneous functionals of the Brownian bridge , 1999 .

[264]  J. Pitman Coalescents with multiple collisions , 1999 .

[265]  O. Kallenberg Ballot theorems and Sojourn laws for stationary processes , 1999 .

[266]  S. Gueron,et al.  The Equilibrium Behavior of Reversible Coagulation-Fragmentation Processes , 1999 .

[267]  Michael Drmota,et al.  Strata of random mappings – A combinatorial approach , 1999 .

[268]  J. L. Gall,et al.  Spatial Branching Processes, Random Snakes, and Partial Differential Equations , 1999 .

[269]  Serik Sagitov,et al.  The general coalescent with asynchronous mergers of ancestral lines , 1999 .

[270]  Eric M. Rains,et al.  Symmetrized Random Permutations , 1999 .

[271]  M. Yor,et al.  A version of Pitman's 2M-X theorem for geometric Brownian motions , 1999 .

[272]  D. Aldous Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists , 1999 .

[273]  J. Pitman The SDE solved by local times of a brownian excursion or bridge derived from the height profile of a random tree or forest , 1999 .

[274]  Guy Louchard,et al.  The Brownian excursion multi-dimensional local time density , 1999, Journal of Applied Probability.

[275]  J. Bertoin Subordinators: Examples and Applications , 1999 .

[276]  J. Pitman Brownian Motion, Bridge, Excursion, and Meander Characterized by Sampling at Independent Uniform Times , 1999 .

[277]  J. Pitman,et al.  Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions , 1999, math/9912170.

[278]  Jean Bertoin,et al.  A fragmentation process connected to Brownian motion , 2000 .

[279]  J. L. Gall Random Trees And Spatial Branching Processes , 2000 .

[280]  Götz Kersting,et al.  A Random Walk Approach to Galton–Watson Trees , 2000 .

[281]  J. Bertoin,et al.  The Bolthausen–Sznitman coalescent and the genealogy of continuous-state branching processes , 2000 .

[282]  J. Pitman,et al.  Two Coalescents Derived from the Ranges of Stable Subordinators , 2000 .

[283]  J. Geiger Poisson point process limits in size-biased Galton-Watson trees , 2000 .

[284]  Jim Pitman,et al.  Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities , 2000 .

[285]  F. Hiai,et al.  The semicircle law, free random variables, and entropy , 2006 .

[286]  A. Hald The Early History of the Cumulants and the Gram‐Charlier Series , 2000 .

[287]  Svante Janson,et al.  Random graphs , 2000, ZOR Methods Model. Oper. Res..

[288]  Jim Pitman,et al.  Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent , 2000 .

[289]  Bernhard Gittenberger,et al.  On the local time density of the reflecting Brownian bridge , 2000 .

[290]  H. Kaspi,et al.  A Ray-Knight theorem for symmetric Markov processes , 2000 .

[291]  R. Wolpert Lévy Processes , 2000 .

[292]  D. Hobson Marked excursions and random trees , 2000 .

[293]  The moments of the area under reflected Brownian bridgeconditional on its local time at zero , 2000 .

[294]  An Extension of Vervaat's Transformation and Its Consequences , 2000 .

[295]  P. Ressel,et al.  Exchangeable Random Orders and Almost Uniform Distributions , 2000 .

[296]  Jason Schweinsberg Coalescents with Simultaneous Multiple Collisions , 2000 .

[297]  A. Etheridge,et al.  An introduction to superprocesses , 2000 .

[298]  O. Zeitouni,et al.  Asymptotics of Certain Coagulation-Fragmentation Processes and Invariant Poisson-Dirichlet Measures , 2001, math/0105111.

[299]  Neil O'Connell,et al.  Pitman's $2M-X$ Theorem for Skip-Free Random Walks with Markovian Increments , 2001 .

[300]  M. Yor,et al.  An Infinite-Dimensional Analogue of the Lebesgue Measure and Distinguished Properties of the Gamma Process , 2001 .

[301]  Martin Möhle,et al.  A Classification of Coalescent Processes for Haploid Exchangeable Population Models , 2001 .

[302]  Konstantin Borovkov,et al.  Kendall's identity for the first crossing time revisited , 2001 .

[303]  Jim Pitman,et al.  Random mappings, forests, and subsets associated with Abel-Cayley-Hurwitz multinomial expansions , 2001 .

[304]  On the path of an inert object impinged on one side by a Brownian particle , 2001 .

[305]  G. Miermont Ordered Additive Coalescent and Fragmentations Associatedto Lévy Processes with No Positive Jumps , 2001 .

[306]  Colm Art O'Cinneide,et al.  Nonuniform random transformations , 2001 .

[307]  Jason E. Fulman Random matrix theory over finite fields , 2001 .

[308]  Philippe Flajolet,et al.  Random maps, coalescing saddles, singularity analysis, and Airy phenomena , 2001, Random Struct. Algorithms.

[309]  J. Bertoin Eternal additive coalescents and certain bridges with exchangeable increments , 2001 .

[310]  Jason Schweinsberg Applications of the continuous-time ballot theorem to Brownian motion and related processes , 2001 .

[311]  Marc Yor,et al.  Brownian analogues of Burke's theorem , 2001 .

[312]  J. Pitman,et al.  On the distribution of ranked heights of excursions of a Brownian bridge , 2001 .

[313]  Anatoly M. Vershik,et al.  The Limit Shape and Fluctuations of Random Partitions of Naturals with Fixed Number of Summands , 2001 .

[314]  Alexander Gnedin,et al.  A Characterization of GEM Distributions , 2001, Combinatorics, Probability and Computing.

[315]  Philippe Chassaing,et al.  Parking Functions, Empirical Processes, and the Width of Rooted Labeled Trees , 2001, Electron. J. Comb..

[316]  Svante Janson,et al.  A Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0 , 2001 .

[317]  J. Bertoin Homogeneous fragmentation processes , 2001 .

[318]  Jim Pitman,et al.  Asymptotics of the Hurwitz Binomial Distribution Related to Mixed Poisson Galton–Watson Trees , 2001, Combinatorics, Probability and Computing.

[319]  Thomas Duquesne,et al.  Random Trees, Levy Processes and Spatial Branching Processes , 2002 .

[320]  J. Pitman,et al.  Invariance Principles for Non-Uniform Random Mappings and Trees , 2002 .

[321]  Neil O'Connell,et al.  Non-Colliding Random Walks, Tandem Queues, and DiscreteOrthogonal Polynomial Ensembles , 2002 .

[322]  Philippe Chassaing,et al.  Random planar lattices and integrated superBrownian excursion , 2002, math/0205226.

[323]  Neil O'Connell,et al.  A path-transformation for random walks and the Robinson-Schensted correspondence , 2002, math/0203177.

[324]  Jim Pitman,et al.  Forest Volume Decompositions and Abel - Cayley - Hurwitz Multinomial Expansions , 2002, J. Comb. Theory, Ser. A.

[325]  Jean Bertoin,et al.  Self-similar fragmentations , 2002 .

[326]  STOCHASTIC FRAGMENTATION AND SOME SUFFICIENT CONDITIONS FOR SHATTERING TRANSITION , 2002 .

[327]  Guy Louchard,et al.  Phase Transition for Parking Blocks, Brownian Excursion and Coalescence , 2022 .

[328]  J. Pitman,et al.  The asymptotic distribution of the diameter of a random mapping , 2002 .

[329]  Jim Pitman,et al.  Poisson–Dirichlet and GEM Invariant Distributions for Split-and-Merge Transformations of an Interval Partition , 2002, Combinatorics, Probability and Computing.

[330]  P. Bougerol,et al.  Paths in Weyl chambers and random matrices , 2002 .

[331]  Richard P. Stanley,et al.  A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron , 2002, Discret. Comput. Geom..

[332]  Marc Yor,et al.  A Representation for Non-Colliding Random Walks , 2002 .

[333]  Lancelot F. James,et al.  Poisson Process Partition Calculus with Applications to Exchangeable Models and Bayesian Nonparametrics , 2002 .

[334]  Neil O'Connell,et al.  Random matrices, non-colliding processes and queues , 2002, math/0203176.

[335]  G. Miermont Self-similar fragmentations derived from the stable tree I , 2003, math/0405168.

[336]  A. Mokkadem,et al.  Ladder variables, internal structure of Galton–Watson trees and finite branching random walks , 2003, Journal of Applied Probability.

[337]  Lancelot F. James Bayesian calculus for gamma processes with applications to semiparametric intensity models , 2003 .

[338]  Thomas Duquesne A limit theorem for the contour process of condidtioned Galton--Watson trees , 2003 .

[339]  A. Vershik,et al.  Harmonic analysis on the infinite symmetric group , 2003, math/0312270.

[340]  Neil O'Connell,et al.  Conditioned random walks and the RSK correspondence , 2003 .

[341]  J. Pitman,et al.  Regenerative composition structures , 2003, math/0307307.

[342]  J. Pitman Poisson-Kingman partitions , 2002, math/0210396.

[343]  R. Arratia,et al.  Logarithmic Combinatorial Structures: A Probabilistic Approach , 2003 .

[344]  M. Marcus,et al.  New perspectives on Ray's theorem for the local times of diffusions , 2003 .

[345]  Self-similar fragmentations and stable subordinators , 2003 .

[346]  Jason Schweinsberg Coalescent processes obtained from supercritical Galton-Watson processes , 2003 .

[347]  A. Mokkadem,et al.  States Spaces of the Snake and Its Tour—Convergence of the Discrete Snake , 2003 .

[348]  Jim Pitman,et al.  The two-parameter generalization of Ewens' random partition structure , 2003 .

[349]  J. Bertoin The asymptotic behavior of fragmentation processes , 2003 .

[350]  P. Diaconis,et al.  The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations , 2003, math/0305313.

[351]  Bénédicte Haas Loss of mass in deterministic and random fragmentations , 2003 .

[352]  Jean-François Marckert,et al.  The depth first processes of Galton--Watson trees converge to the same Brownian excursion , 2003 .

[353]  Jim Pitman,et al.  Path transformations of first passage bridges , 2003 .

[354]  Lancelot F. James,et al.  Generalized weighted Chinese restaurant processes for species sampling mixture models , 2003 .

[355]  J. Pitman,et al.  Infinitely Divisible Laws Associated with Hyperbolic Functions , 2003, Canadian Journal of Mathematics.

[356]  J. Bertoin,et al.  Stochastic flows associated to coalescent processes , 2003 .

[357]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae (Second Edition) , 2003 .

[358]  S. Kerov,et al.  Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis , 2003 .

[360]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[361]  Dual Random Fragmentation and Coagulation and an Application to the Genealogy of Yule Processes , 2004, math/0408128.

[362]  Bénédicte Haas Regularity of formation of dust in self-similar fragmentations , 2004 .

[363]  Rick Durrett,et al.  A coalescent model for the effect of advantageous mutations on the genealogy of a population , 2004, math/0411071.

[364]  J. Pitman,et al.  Rayleigh processes, real trees, and root growth with re-grafting , 2004, math/0402293.

[365]  . N.S.F.GrantsDmsandDms,et al.  Brownian Bridge Asymptotics for Random p-Mappings , 2004 .

[366]  Julien Berestycki,et al.  Exchangeable Fragmentation-Coalescence Processes and their Equilibrium Measures , 2004, math/0403154.

[367]  G. Miermont,et al.  The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree , 2004, math/0401028.

[368]  J. L. Gall,et al.  Probabilistic and fractal aspects of Lévy trees , 2005, math/0501079.

[369]  J. Bertoin,et al.  Stochastic flows associated to coalescent processes II: Stochastic differential equations , 2005 .

[370]  Coagulation-fragmentation duality, Poisson-Dirichlet distributions and random recursive trees , 2005, math/0507591.

[371]  S. Zabell Symmetry and Its Discontents: The Continuum of Inductive Methods Revisited , 2005 .

[372]  Self-similar fragmentations derived from the stable tree II: splitting at nodes , 2004, math/0405170.

[373]  Martin Möhle,et al.  Alpha-Stable Branching and Beta-Coalescents , 2005 .

[374]  Christina Goldschmidt,et al.  Random Recursive Trees and the Bolthausen-Sznitman Coalesent , 2005, math/0502263.

[375]  Ranked Fragmentations , 2006, math/0604523.

[376]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[377]  S. Kerov Coherent random allocations, and the Ewens-Pitman formula , 2006 .

[378]  Alexander Gnedin,et al.  Asymptotic laws for compositions derived from transformed subordinators , 2006 .

[379]  Vijaya Ramachandran,et al.  The diameter of sparse random graphs , 2007, Random Struct. Algorithms.

[380]  Jason Schweinsberg ELECTRONIC COMMUNICATIONS in PROBABILITY A NECESSARY AND SUFFICIENT CONDITION FOR THE Λ-COALESCENT TO COME DOWN FROM IN- FINITY. , 2022 .

[381]  L. Takács,et al.  Brownian local times , 1995 .

[382]  CONTOUR PROCESSES OF RANDOM TREES , .