Percolation and disordered systems

[1]  Percolation with several defect types. An estimate of critical probability for a square lattice , 1989 .

[2]  Olle Hggstrm The random-cluster model on a homogeneous tree , 1996 .

[3]  T. Liggett Multiple transition points for the contact process on the binary tree , 1996 .

[4]  Lower Bounds on the Connectivity Function in all Directions for Bernoulli Percolation in Two and Three Dimensions , 1990 .

[5]  Geoffrey Grimmett,et al.  Critical probabilities for site and bond percolation models , 1998 .

[6]  C. Preston Gibbs States on Countable Sets , 1974 .

[7]  Percolation of the minority spins in high-dimensional Ising models , 1987 .

[8]  Charles M. Newman,et al.  Superdiffusivity in first-passage percolation , 1996 .

[9]  Newman,et al.  Broken symmetry and domain structure in Ising-like systems. , 1990, Physical review letters.

[10]  G. Grimmett,et al.  Random walks in random labyrinths , 1996 .

[11]  L. Percolation and ferromagnetism on Z 2 : the q-state Potts cases ’ , 1996 .

[12]  H. A. Lorentz The motion of electrons in metallic bodies I , 1904 .

[13]  L. Chayes,et al.  The density of interfaces: a new first-passage problem , 1993, Journal of Applied Probability.

[14]  Rick Durrett,et al.  Large deviations for the contact process and two dimensional percolation , 1988 .

[15]  J. Chayes,et al.  Exponential decay of connectivities in the two-dimensional ising model , 1987 .

[16]  G. Grimmett,et al.  Strict inequality for critical values of Potts models and random-cluster processes , 1993 .

[17]  L. Chayes On the absence of directed fractal percolation , 1995 .

[18]  D. Stauffer Scaling properties of percolation clusters , 1981 .

[19]  K. Alexander,et al.  Approximation of subadditive functions and convergence rates in limiting-shape results , 1997 .

[20]  J. Berg A constructive mixing condition for $2$-D Gibbs measures with random interactions , 1997 .

[21]  Decay Of Correlations In Subcritical Potts And Random-Cluster Models , 1996 .

[22]  Robin Pemantle,et al.  Unpredictable paths and percolation , 1998 .

[23]  J. Wierman Directed Site Percolation and Dual Filling Models , 1987 .

[24]  S. Varadhan,et al.  Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions , 1986 .

[25]  H. Kesten,et al.  A central limit theorem for “critical” first-passage percolation in two dimensions , 1997 .

[26]  Newman,et al.  Multiple states and thermodynamic limits in short-ranged Ising spin-glass models. , 1992, Physical review. B, Condensed matter.

[27]  C. Newman Some critical exponent inequalities for percolation , 1986 .

[28]  H. Kesten,et al.  Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation , 1987 .

[29]  E. Cohen,et al.  Normal and abnormal diffusion in Ehrenfest's wind-tree model , 1967 .

[30]  Van den Berg,et al.  Inequalities with applications to percolation and reliability , 1985, Journal of Applied Probability.

[31]  C. Nash-Williams,et al.  Random walk and electric currents in networks , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[32]  Duality for k-Degree Percolation on the Square Lattice , 1987 .

[33]  H. Kesten Scaling relations for 2D-percolation , 1987 .

[34]  Gordon Slade,et al.  The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions , 1995, Combinatorics, Probability and Computing.

[35]  H. Kesten,et al.  BEHAVIOR IN LARGE DIMENSIONS OF THE POTTS AND HEISENBERG MODELS , 1989 .

[36]  Thomas M. Liggett,et al.  Improved Upper Bounds for the Contact Process Critical Value , 1995 .

[37]  G. Grimmett Differential Inequalities for Potts and Random-Cluster Processes , 1993 .

[38]  Terry Lyons A Simple Criterion for Transience of a Reversible Markov Chain , 1983 .

[39]  A. Sidorenko,et al.  Percolation theory and some applications , 1988 .

[40]  K. Alexander,et al.  Stability of the Wulff minimum and fluctuations in shape for large finite clusters in two-dimensional percolation , 1992 .

[41]  F. Wang,et al.  Novel phenomena in Lorentz lattice gases , 1995 .

[42]  Topics in percolation , 1991 .

[43]  On the absence of infinite AB percolation clusters in bipartite graphs , 1987 .

[44]  J. Michael Steele,et al.  Asymptotics for Euclidean minimal spanning trees on random points , 1992 .

[45]  D. H. Martirosian Translation invariant Gibbs states in theq-state Potts model , 1986 .

[46]  M. Penrose,et al.  The random connection model in high dimensions , 1997 .

[47]  Ground-state structure in a highly disordered spin-glass model , 1995, adap-org/9505005.

[48]  J. van den Berg,et al.  A new lower bound for the critical probability of site percolation on the square lattice , 1996, Random Struct. Algorithms.

[49]  Disjoint Occurrences of Events: Results and Conjectures , 1985 .

[50]  Rahul Roy,et al.  Uniqueness of unbounded occupied and vacant components in Boolean models , 1994 .

[51]  E. Cohen,et al.  New types of diffusion in lattice gas cellular automata , 1993 .

[52]  Y. Higuchi A remark on the percolation for the 2D Ising model , 1989 .

[53]  EQUALITY OF CRITICAL DENSITIES IN CONTINUUM PERCOLATION , 1995 .

[54]  R. Schinazi,et al.  A complete convergence theorem for an epidemic model , 1996, Journal of Applied Probability.

[55]  K. Falconer Sets with Prescribed Projections and Nikodym Sets , 1986 .

[56]  H. Kramers,et al.  Collected scientific papers , 1956 .

[57]  R. Pemantle Choosing a Spanning Tree for the Integer Lattice Uniformly , 1991, math/0404043.

[58]  Bernard Derrida,et al.  PROBABILITY AND PHASE TRANSITION , 1994 .

[59]  R. Kotecký Geometric Representation of Lattice Models and Large Volume Asymptotics , 1994 .

[60]  Y. Higuchi Level set representation for the Gibbs states of the ferromagnetic ising model , 1991 .

[61]  Mathew D. Penrose Continuum percolation and Euclidean minimal spanning trees in high dimensions , 1996 .

[62]  Yu Zhang,et al.  Random walk on the infinite cluster of the percolation model , 1993 .

[63]  L. Russo A note on percolation , 1978 .

[64]  Kantor,et al.  Topological entanglements in the percolation problem. , 1988, Physical review letters.

[65]  R. Lyons Random Walks and Percolation on Trees , 1990 .

[66]  R. Pemantle,et al.  On which Graphs are All Random Walks in Random Environments Transient , 2004, math/0404087.

[67]  G. Grimmett,et al.  The Critical Contact Process Dies Out , 1990 .

[68]  H. Kesten A Scaling relation at criticality for 2D-Percolation , 1987 .

[69]  Jennifer Chayes,et al.  Gaussian fluctuations of connectivities in the subcritical regime of percolation , 1991 .

[70]  Michael Aizenman,et al.  Percolation Critical Exponents Under the Triangle Condition , 1991 .

[71]  Continuity of percolation probability in ∞ + 1 dimensions , 1996 .

[72]  A note on differentiability of the cluster density for independent percolation in high dimensions , 1992 .

[73]  R. P. Langlands,et al.  On the universality of crossing probabilities in two-dimensional percolation , 1992 .

[74]  Senya Shlosman,et al.  First-order phase transitions in large entropy lattice models , 1982 .

[75]  Michael Aizenman,et al.  On the Number of Incipient Spanning Clusters , 1997 .

[76]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[77]  Infinite AB percolation clusters exist on the triangular lattice , 1987 .

[78]  Fontes,et al.  Surface deconstruction and roughening in the multiziggurat model of wetting. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  C. Newman Disordered Ising Systems and Random Cluster Representations , 1994 .

[80]  On the phase transition to sheet percolation in random Cantor sets , 1996 .

[81]  Yu Zhang,et al.  The Probability of a Large Finite Cluster in Supercritical Bernoulli Percolation , 1990 .

[82]  Y. Saint-Aubin,et al.  Conformal invariance in two-dimensional percolation , 1994, math/9401222.

[83]  R. B. Potts Some generalized order-disorder transformations , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[84]  Kari Kuulasmaa,et al.  The spatial general epidemic and locally dependent random graphs , 1982, Journal of Applied Probability.

[85]  Yu Zhang Divergence of the bulk resistance at criticality in disordered media , 1996 .

[86]  Russell Lyons,et al.  Correction: Random walk in a random environment and first-passage percolation on trees , 1992 .

[87]  Y. Peres,et al.  Random walks on a tree and capacity in the interval , 1992 .

[88]  M. Aizenman,et al.  Geometric analysis of ϕ 4 fields and Ising models , 1982 .

[89]  J. Wierman Equality of directional critical exponents in multiparameter percolation models , 1994 .

[90]  J. Chayes,et al.  The large-N limit of the threshold values in Mandelbrot's fractal percolation process , 1989 .

[91]  Newman Tj Exact results for a model of interface growth. , 1995 .

[92]  John C. Wierman Equality of the Bond Percolation Critical Exponents for Two Pairs of Dual Lattices , 1992, Comb. Probab. Comput..

[93]  Maury Bramson,et al.  The Contact Processes in a Random Environment , 1991 .

[94]  Yu Zhang A Shape Theorem for Epidemics and Forest Fires with Finite Range Interactions , 1993 .

[95]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1997, Networks.

[96]  C. Newman,et al.  Chaotic size dependence in spin glasses , 1993 .

[97]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[98]  Geoffrey Grimmett,et al.  On the geometry of random Cantor sets and fractal percolation , 1992 .

[99]  R. Pemantle,et al.  Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings Via Transfer-Impedances , 1993, math/0404048.

[100]  P. Whittle,et al.  Polymer models and generalized Potts-Kasteleyn models , 1994 .

[101]  R. Pemantle,et al.  Martin capacity for Markov chains , 1995, math/0404054.

[102]  Zhang The fractal volume of the two-dimensional invasion percolation cluster , 1995 .

[103]  G. Grimmett,et al.  The supercritical phase of percolation is well behaved , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[104]  J. Thomson Collected Scientific Papers , 1920, Nature.

[105]  Van den Berg,et al.  On a Combinatorial Conjecture Concerning Disjoint Occurrences of Events , 1987 .

[106]  C. Fortuin,et al.  Correlation inequalities on some partially ordered sets , 1971 .

[107]  Christian Borgs,et al.  The Birth of the Infinite Cluster:¶Finite-Size Scaling in Percolation , 2001 .

[108]  G. Kalai,et al.  Every monotone graph property has a sharp threshold , 1996 .

[109]  Charles M. Newman,et al.  A Surface View of First-Passage Percolation , 1995 .

[110]  Van den Berg,et al.  Inequalities for the Time Constant in First-Passage Percolation , 1993 .

[111]  C. Newman,et al.  Surfaces and Peierls contours: 3-d wetting and 2-d Ising percolation , 1989 .

[112]  Charles M. Newman,et al.  The trapping transition in dynamic (invasion) and static percolation , 1990 .

[113]  Rick Durrett,et al.  Ten lectures on particle systems , 1995 .

[114]  J. Berg,et al.  Percolation and the hard-core lattice gas model , 1994 .

[115]  A. Stacey The existence of an intermediate phase for the contact process on trees , 1996 .

[116]  T. E. Harris A lower bound for the critical probability in a certain percolation process , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[117]  L. Chayes On the length of the shortest crossing in the super-critical phase of Mandelbrot's percolation process , 1996 .

[118]  Yu Zhang,et al.  A Limit Theorem for $N_{0n}/n$ in First-Passage Percolation , 1984 .

[119]  Jeffrey E. Steif,et al.  On the continuity of the critical value for long range percolation in the exponential case , 1996 .

[120]  Thomas M. Liggett,et al.  The Periodic Threshold Contact Process , 1991 .

[121]  H. Kesten Asymptotics in High Dimensions For the Fortuin-Kasteleyn Random Cluster Model , 1991 .

[122]  Russell Lyons,et al.  Random walk in a random environment and rst-passage percolation on trees , 1992 .

[123]  M. V. Men'shikov,et al.  Quantitative Estimates and Rigorous Inequalities for Critical Points of a Graph and Its Subgraphs , 1987 .

[124]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[125]  R. Schonmann Theorems and Conjectures on the Droplet-Driven Relaxation of Stochastic Ising Models , 1994 .

[126]  Ronald W. J. Meester,et al.  Stability Properties of a Flow Process in Graphs , 1991, Random Struct. Algorithms.

[127]  F. M. Dekking,et al.  Superbranching processes and projections of random Cantor sets , 1988 .

[128]  Yuval Peresy,et al.  Dynamical Percolation , 1996 .

[129]  Michael E. Fisher,et al.  Critical Probabilities for Cluster Size and Percolation Problems , 1961 .

[130]  M. Fiocco,et al.  Parameter estimation for the supercritical contact process , 2003 .

[131]  J. Ashkin,et al.  Two Problems in the Statistical Mechanics of Crystals. I. The Propagation of Order in Crystal Lattices. I. The Statistics of Two-Dimensional Lattices with Four Components. , 1943 .

[132]  Coexistence of infinite (*)-clusters II. Ising percolation in two dimensions , 1993 .

[133]  G. Grimmett,et al.  The random-cluster model on the complete graph , 1996 .

[134]  Enrique D. Andjel Characteristic Exponents for Two-Dimensional Bootstrap Percolation , 1993 .

[135]  Peter G. Doyle,et al.  Random Walks and Electric Networks: REFERENCES , 1987 .

[136]  AB percolation: a brief survey , 1989 .

[137]  Newman,et al.  Spatial inhomogeneity and thermodynamic chaos. , 1995, Physical Review Letters.

[138]  James Allen Fill,et al.  PERCOLATION, FIRST-PASSAGE PERCOLATION, AND COVERING TIMES FOR RICHARDSON'S MODEL ON THE n-CUBE (Short title: PERCOLATION ON THE CUBE) , 1993 .

[139]  J. Berg,et al.  A uniqueness condition for Gibbs measures, with application to the 2-dimensional Ising antiferromagnet , 1993 .

[140]  J. Wierman,et al.  AB percolation on bond-decorated graphs , 1993, Journal of Applied Probability.

[141]  Ãgoston Pisztora,et al.  Surface order large deviations for Ising, Potts and percolation models , 1996 .

[142]  Leonid A. Bunimovich,et al.  Recurrence properties of Lorentz lattice gas cellular automata , 1992 .

[143]  J. Wierman On AB percolation on bipartite graphs , 1988 .

[144]  L. Chayes Percolation and ferromagnetism on Z2: the q-state Potts cases☆ , 1996 .

[145]  Van den Berg,et al.  On the Continuity of the Percolation Probability Function , 1984 .

[146]  REMARKS ON A RANDOM SURFACE , 1991 .

[147]  J. Chayes,et al.  Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models , 1988 .

[148]  Jennifer Chayes,et al.  On the upper critical dimension of Bernoulli percolation , 1987 .

[149]  H. Poincaré,et al.  Percolation ? , 1982 .

[150]  K. Alexander Finite clusters in high-density continuous percolation: Compression and sphericality , 1993 .

[151]  John C. Wierman,et al.  Substitution Method Critical Probability Bounds for the Square Lattice Site Percolation Model , 1995, Combinatorics, Probability and Computing.

[152]  Charles M. Newman,et al.  An intermediate phase with slow decay of correlations in one dimensional 1/|x−y|2 percolation, Ising and Potts models , 1988 .

[153]  David Bruce Wilson,et al.  Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996, Random Struct. Algorithms.

[154]  A. Sokal,et al.  Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. , 1988, Physical review. D, Particles and fields.

[155]  P. Ferrari,et al.  An invariance principle for reversible Markov processes. Applications to random motions in random environments , 1989 .

[156]  Jennifer Chayes,et al.  The analysis of the Widom-Rowlinson model by stochastic geometric methods , 1995 .

[157]  I. Benjamini,et al.  Percolation of Arbitrary Words in $\{0, 1\}^\mathbb{N}$ , 1995 .

[158]  D. Welsh,et al.  Percolation in the random cluster process and Q-state Potts model , 1993 .

[159]  F. Y. Wu,et al.  Exact results for the Potts model in two dimensions , 1978 .

[160]  H. Kesten Aspects of first passage percolation , 1986 .

[161]  Harry Kesten,et al.  Percolation Theory and Ergodic Theory of Infinite Particle Systems , 1987 .

[162]  C. Newman Percolation theory: A selective survey of rigorous results , 1986 .

[163]  R. Durrett,et al.  The Contact Process on a Finite Set. III: The Critical Case , 1989 .

[164]  Thomas M. Liggett,et al.  Survival of Discrete Time Growth Models, with Applications to Oriented Percolation , 1995 .

[165]  C. Newman,et al.  The wetting transition in a random surface model , 1991 .

[166]  N. Madras,et al.  THE SELF-AVOIDING WALK , 2006 .

[167]  Charles M. Newman,et al.  Percolation in half-spaces: equality of critical densities and continuity of the percolation probability , 1991 .

[168]  Olle Häggström,et al.  Asymptotic shapes for stationary first passage percolation , 1995 .

[169]  C. Newman Another critical exponent inequality for percolation: β⩾2/δ , 1987 .

[170]  D. Welsh,et al.  Percolation probabilities on the square lattice , 1978 .

[171]  H. Kesten Percolation theory for mathematicians , 1982 .

[172]  M. Aizenman,et al.  The phase transition in a general class of Ising-type models is sharp , 1987 .

[173]  Abel Klein Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment , 1994 .

[174]  Charles M. Newman,et al.  Percolation in ∞ + 1 dimensions , 1990 .

[175]  AB percolation on close-packed graphs , 1988 .

[176]  R. Pemantle,et al.  Planar First-Passage Percolation Times are not Tight , 2004, math/0404050.

[177]  Kenneth S. Alexander,et al.  Percolation and minimal spanning forests in infinite graphs , 1995 .

[178]  R. Langlands An essay on the dynamics and statistics of critical field theories , 1996 .

[179]  T. Ruijgrok,et al.  Deterministic lattice gas models , 1988 .

[180]  E. Lieb A refinement of Simon's correlation inequality , 1980 .

[181]  K. Falconer Projections of random Cantor sets , 1989 .

[182]  Yu Zhang A Note on Inhomogeneous Percolation , 1994 .

[183]  Harry Kesten,et al.  Percolation Theory and First-Passage Percolation , 1987 .

[184]  G. Slade,et al.  The triangle condition for percolation , 1989 .

[185]  J. Berg A note on disjoint-occurrence inequalities for marked Poisson point processes , 1996 .

[186]  David Griffeath,et al.  Additive and Cancellative Interacting Particle Systems , 1979 .

[187]  Newman,et al.  Spin-glass model with dimension-dependent ground state multiplicity. , 1994, Physical review letters.

[188]  C. Newman,et al.  Persistent survival of one-dimensional contact processes in random environments , 1996 .

[189]  R. Pemantle The Contact Process on Trees , 1992, math/0404046.

[190]  Harry Kesten,et al.  On the time constant and path length of first-passage percolation , 1980, Advances in Applied Probability.

[191]  Newman,et al.  Non-mean-field behavior of realistic spin glasses. , 1995, Physical review letters.

[192]  G. Grimmett,et al.  A central limit theorem for random walks in random labyrinths , 1999 .

[193]  Yuval Peres,et al.  Tree-indexed random walks on groups and first passage percolation , 1994 .

[194]  Geoffrey Grimmett,et al.  Exponential decay for subcritical contact and percolation processes , 1991 .

[195]  G. Grimmett The Stochastic Random-Cluster Process and the Uniqueness of Random-Cluster Measures , 1995 .

[196]  Russell Lyons,et al.  Random Walks, Capacity and Percolation on Trees , 1992 .

[197]  J. Hammersley Percolation Processes: Lower Bounds for the Critical Probability , 1957 .

[198]  R. Durrett,et al.  Correlation lengths for oriented percolation , 1989 .

[199]  Barry Simon,et al.  Correlation inequalities and the decay of correlations in ferromagnets , 1980 .

[200]  John Cardy Critical percolation in finite geometries , 1992 .

[201]  C. Newman,et al.  Recent exact results on wetting , 1990 .

[202]  Charles M. Newman,et al.  Infinite clusters in percolation models , 1981 .

[203]  Newman,et al.  Broken ergodicity and the geometry of rugged landscapes. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[204]  C. Newman The 1/r2 phase transition: a review , 1989 .

[205]  Gordon Slade,et al.  Mean-Field Behaviour and the Lace Expansion , 1994 .

[206]  The complete convergence theorem of the contact process on trees , 1996 .

[207]  Domination Between Trees and Application to an Explosion Problem , 2004, math/0404044.

[208]  Ronald W. J. Meester An algorithm for calculating critical probabilities and percolation functions in percolation models defined by rotations , 1989 .

[209]  R. Durrett,et al.  Critical behavior of the two-dimensional first passage time , 1986 .

[210]  R. Meester,et al.  Nonuniversality and continuity of the critical covered volume fraction in continuum percolation , 1994 .

[211]  Michael Aizenman,et al.  Geometric analysis of φ4 fields and Ising models. Parts I and II , 1982 .

[212]  Jean Ruiz,et al.  Phases coexistence and surface tensions for the potts model , 1986 .

[213]  F. Wang,et al.  Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices , 1995, comp-gas/9501006.

[214]  Geoffrey Grimmett,et al.  Strict monotonicity for critical points in percolation and ferromagnetic models , 1991 .

[215]  S. Lang Complex Analysis , 1977 .

[216]  Rick Durrett,et al.  Connectivity properties of Mandelbrot's percolation process , 1988 .

[217]  Harry Kesten,et al.  Asymptotics in High Dimensions for Percolation , 1990 .

[218]  Van den Berg,et al.  Disagreement percolation in the study of Markov fields , 1994 .

[219]  L. Onsager Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[220]  A sharp transition for the two-dimensional Ising percolation , 1993 .

[221]  Michael Aizenman,et al.  On the critical behavior of the magnetization in high-dimensional Ising models , 1986 .

[222]  J. T. Chayes,et al.  The Mean Field Bound for the Order Parameter of Bernoulli Percolation , 1987 .

[223]  G. Grimmett Potts models and random-cluster processes with many-body interactions , 1994 .

[224]  F. Y. Wu The Potts model , 1982 .

[225]  Kenneth S. Alexander,et al.  Percolation of level sets for two-dimensional random fields with lattice symmetry , 1994 .

[226]  T. Liggett Coexistence in Threshold Voter Models , 1994 .

[227]  Hans-Otto Georgii,et al.  Gibbs Measures and Phase Transitions , 1988 .

[228]  Lahoussine Laanait,et al.  Interfaces in the Potts model I: Pirogov-Sinai theory of the Fortuin-Kasteleyn representation , 1991 .

[229]  Charles M. Newman,et al.  Geodesics in two-dimensional first-passage percolation , 1996 .

[230]  Y. Midzuno,et al.  Statistics of Two-Dimensional Lattices with Many Components , 1954 .

[231]  S. Shlosman,et al.  Aggregation and intermediate phases in dilute spin systems , 1995 .

[232]  C. Newman,et al.  First Passage Percolation for Random Colorings of $\mathbb{Z}^d$ , 1993 .

[233]  R. Durrett Lecture notes on particle systems and percolation , 1988 .

[234]  C. Fortuin,et al.  On the random-cluster model: I. Introduction and relation to other models , 1972 .

[235]  Neal Madras,et al.  On the Critical Behavior of the Contact Process in Deterministic Inhomogeneous Environments , 1994 .

[236]  K. Mosler,et al.  Stochastic orders and decision under risk , 1991 .

[237]  M. Penrose,et al.  Large deviations for discrete and continuous percolation , 1996, Advances in Applied Probability.

[238]  C. Newman,et al.  Markov fields on branching planes , 1990 .

[239]  Yoshiharu Kohayakawa,et al.  Percolation in High Dimensions , 1994, Eur. J. Comb..

[240]  Phase transitions in Mandelbrot's percolation process in three dimensions , 1991 .

[241]  G. Slade,et al.  Mean-field critical behaviour for percolation in high dimensions , 1990 .

[242]  C. Fortuin,et al.  On the random-cluster model II. The percolation model , 1972 .

[243]  C. Newman,et al.  Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses , 1992 .

[244]  Michael E. Fisher,et al.  Critical Exponents for Long-Range Interactions , 1972 .

[245]  L. Russo On the critical percolation probabilities , 1981 .

[246]  K. Alexander A Note on Some Rates of Convergence in First-Passage Percolation , 1993 .

[247]  J. Friedlander Bounds for L-Functions , 1995 .

[248]  Harry Kesten,et al.  Greedy Lattice Animals II: Linear Growth , 1994 .

[249]  L. Chayes The density of Peierls contours in d=2 and the height of Wedding Cake , 1993 .

[250]  R. Pemantle,et al.  First passage percolation and a model for competing spatial growth , 1997, Journal of Applied Probability.

[251]  L. Russo An approximate zero-one law , 1982 .

[252]  Y. Sinai,et al.  Phase diagrams of classical lattice systems , 1975 .

[253]  Geoffrey Grimmett The Rank Polynomials of Large Random Lattices , 1978 .

[254]  Harry Kesten,et al.  The Correlation Length for the High-Density Phase of Bernoulli Percolation , 1989 .

[255]  Yu Zhang A Power Law for Connectedness of Some Random Graphs at the Critical Point , 1991, Random Struct. Algorithms.

[256]  The density of Peierls contours in d = 2 and the height of the Wedding Cake , 1992 .

[257]  J. W. Essam,et al.  Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions , 1964 .

[258]  Failure of the power laws on some subgraphs of the Z2 lattice , 1992 .

[259]  J. Chayes,et al.  The phase boundary in dilute and random Ising and Potts ferromagnets , 1987 .

[260]  Random walk in a strongly inhomogeneous environment and invasion percolation , 1995 .

[261]  Exotic states in long-range spin glasses , 1993 .

[262]  Y. Sinai,et al.  Phase diagrams of classical lattice systems continuation , 1976 .

[263]  Jennifer Chayes,et al.  The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation , 1990 .

[264]  Claudia Neuhauser,et al.  Epidemics with Recovery in $D = 2$ , 1991 .

[265]  Itai Benjamini,et al.  Conformal Invariance of Voronoi Percolation , 1998 .

[266]  Infinite AB percolation clusters exist , 1987 .

[267]  Charles M. Newman,et al.  Bernoulli Percolation Above Threshold: An Invasion Percolation Analysis , 1987 .

[268]  H. Kesten The critical probability of bond percolation on the square lattice equals 1/2 , 1980 .

[269]  C. Newman Inequalities for γ and Related Critical Exponents in Short and Long Range Percolation , 1987 .

[270]  H. Kesten Connectivity of certain graphs on halfspaces, quarter spaces, ...· , 1992 .

[271]  J. Chayes,et al.  Correlation length bounds for disordered Ising ferromagnets , 1989 .

[272]  Consistent estimation of percolation quantities , 1998 .

[273]  G. Grimmett,et al.  Dynamic Renormalization and Continuity of the Percolation Transition in Orthants , 1991 .

[274]  E. Ising Beitrag zur Theorie des Ferromagnetismus , 1925 .

[275]  Newman,et al.  Wetting in a three-dimensional system: An exact solution. , 1988, Physical review letters.

[276]  H. Kesten,et al.  A Tribute to Paul Erdős: The critical parameter for connectedness of some random graphs , 1990 .

[277]  Alan D. Sokal,et al.  Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory , 1992 .

[278]  Geoffrey Grimmett,et al.  Dependent random graphs and spatial epidemics , 1998 .

[279]  THE CRITICAL CONTACT PROCESS ON A HOMOGENEOUS TREE , 1994 .

[280]  Robin Pemantle,et al.  Diffusion-limited aggregation on a tree , 1997 .

[281]  C. Borgs,et al.  The covariance matrix of the Potts model: A random cluster analysis , 1994, adap-org/9411001.

[282]  M. Aizenman,et al.  Percolation methods for disordered quantum Ising models , 1993 .

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

[284]  R. Holley Remarks on the FKG inequalities , 1974 .

[285]  Harry Kesten,et al.  Greedy Lattice Animals I: Upper Bounds , 1993 .

[286]  Ronald W. J. Meester,et al.  Long Range Percolation in Stationary Point Processes , 1993, Random Struct. Algorithms.

[287]  F. Wang,et al.  New results for diffusion in Lorentz lattice gas cellular automata , 1995, comp-gas/9501003.

[288]  On the critical behavior of the first passage time in d≥3 , 1991 .

[289]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[290]  R. Durrett,et al.  The Contact Process on a Finite Set. II , 1988 .

[291]  C. Newman Ising models and dependent percolation , 1990 .

[292]  Charles M. Newman,et al.  Tree graph inequalities and critical behavior in percolation models , 1984 .

[293]  Michael Aizenman,et al.  Metastability effects in bootstrap percolation , 1988 .

[294]  Supercritical behaviors in first-passage percolation , 1995 .

[295]  K. Alexander,et al.  On weak mixing in lattice models , 1998 .

[296]  J. Deuschel,et al.  Surface order large deviations for high-density percolation , 1996 .

[297]  R. Burton,et al.  Density and uniqueness in percolation , 1989 .

[298]  Jacobs,et al.  Generic rigidity percolation in two dimensions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[299]  École d'été de probabilités de Saint-Flour,et al.  École d'été de probabilités de Saint-Flour XIII - 1983 , 1985 .

[300]  Thomas M. Liggett,et al.  Spatially Inhomogeneous Contact Processes , 1991 .

[301]  A. Martin-Löf,et al.  On the uniqueness of the equilibrium state for Ising spin systems , 1972 .

[302]  R. Mauldin,et al.  Random recursive constructions: asymptotic geometric and topological properties , 1986 .

[303]  M. Aizenman,et al.  Sharpness of the phase transition in percolation models , 1987 .

[304]  Kenneth S. Alexander,et al.  The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees , 1996 .

[305]  Tomasz Nowicki,et al.  Infinite clusters and critical values in two-dimensional circle percolation , 1989 .

[306]  M. Aizenman,et al.  Geometric aspects of quantum spin states , 1993, cond-mat/9310009.

[307]  C. Fortuin,et al.  Phase transitions in lattice systems with random local properties , 1969 .

[308]  H. Kesten,et al.  Strict inequalities for some critical exponents in two-dimensional percolation , 1987 .

[309]  J. Chayes,et al.  On a sharp transition from area law to perimeter law in a system of random surfaces , 1983 .

[310]  Yu Zhang A Limit Theorem for Matching Random Sequences Allowing Deletions , 1995 .

[311]  Critical probability bounds for two-dimensional site percolation models , 1988 .

[312]  Bond percolation critical probability bounds derived by edge contraction , 1988 .

[313]  LETTER TO THE EDITOR: A crossing probability for critical percolation in two dimensions , 1996, cond-mat/9603167.

[314]  R. Ziff,et al.  Lorentz lattice-gas and kinetic-walk model. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[315]  Uniqueness in percolation theory , 1994 .

[316]  Thomas M. Liggett,et al.  The Survival of One-Dimensional Contact Processes in Random Environments , 1992 .

[317]  Ilya Molchanov,et al.  Random fractals , 1986, Mathematical Proceedings of the Cambridge Philosophical Society.

[318]  Ãgoston Pisztora,et al.  ON THE CHEMICAL DISTANCE FOR SUPERCRITICAL BERNOULLI PERCOLATION , 1996 .

[319]  C. Fortuin On the random-cluster model: III. The simple random-cluster model , 1972 .

[320]  G. Grimmett,et al.  On the uniqueness of the infinite cluster in the percolation model , 1987 .

[321]  Michel Loève,et al.  Probability Theory I , 1977 .

[322]  R. Mauldin,et al.  Exact Hausdorff dimension in random recursive constructions. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[323]  R. Pemantle,et al.  Galton-Watson Trees with the Same Mean Have the Same Polar Sets , 1995, math/0404053.

[324]  R. Meester Connectivity in fractal percolation , 1992 .

[325]  H. Kesten,et al.  The tortuosity of occupied crossings of a box in critical percolation , 1993 .

[326]  Jacobs,et al.  Generic rigidity percolation: The pebble game. , 1995, Physical review letters.

[327]  Y. Peres Intersection-equivalence of Brownian paths and certain branching processes , 1996 .

[328]  Abel Klein,et al.  EXTINCTION OF CONTACT AND PERCOLATION PROCESSES IN A RANDOM ENVIRONMENT , 1994 .

[329]  R. Schonmann,et al.  Domination by product measures , 1997 .

[330]  J. Wierman,et al.  Counterexamples in AB percolation , 1989 .

[331]  Charles M. Newman,et al.  Uniqueness of the infinite cluster and related results in percolation , 1987 .

[332]  École d'été de probabilités de Saint-Flour,et al.  École d'été de probabilités de Saint Flour XIV, 1984 , 1986 .

[333]  J. Hawkes,et al.  Trees Generated by a Simple Branching Process , 1981 .

[334]  C. Newman,et al.  Divergence of Shape Fluctuations in Two Dimensions , 1995 .

[335]  L. Chayes,et al.  Aspects of the Fractal Percolation Process , 1995 .

[336]  F. M. Dekking,et al.  On the structure of Mandelbrot's percolation process and other random cantor sets , 1990 .

[337]  G. Grimmett Comparison and disjoint-occurrence inequalities for random-cluster models , 1995 .

[338]  S. Graf Statistically self-similar fractals , 1987 .