Interacting particles on the line and Dunkl intertwining operator of type A: application to the freezing regime
暂无分享,去创建一个
[1] F. Dyson. A Brownian‐Motion Model for the Eigenvalues of a Random Matrix , 1962 .
[2] Confluent Hypergeometric Orthogonal Polynomials Related to the Rational Quantum Calogero System with Harmonic Confinement , 1996, q-alg/9609032.
[3] Chern-Simons theory, 2d Yang-Mills, and Lie algebra wanderers , 2004, hep-th/0412110.
[4] Charles F. Dunkl,et al. Differential-difference operators associated to reflection groups , 1989 .
[5] H. Spohn,et al. The 1 + 1-dimensional Kardar–Parisi–Zhang equation and its universality class , 2010, 1010.2691.
[6] Ivan Corwin. The Kardar-Parisi-Zhang equation and universality class , 2011, 1106.1596.
[7] Essam,et al. Vicious walkers and directed polymer networks in general dimensions. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[8] Anthony J. Guttmann,et al. Vicious walkers, friendly walkers and Young tableaux: II. With a wall , 2000 .
[9] Anthony J. Guttmann,et al. Vicious walkers and Young tableaux I: without walls , 1998 .
[10] Yuan Xu,et al. Orthogonal Polynomials of Several Variables: Subject index , 2001 .
[11] M. Katori,et al. Noncolliding Brownian Motion and Determinantal Processes , 2007, 0705.2460.
[12] K. Takeuchi,et al. Universal fluctuations of growing interfaces: evidence in turbulent liquid crystals. , 2010, Physical review letters.
[13] N. Demni. Radial Dunkl Processes Associated with Dihedral Systems , 2008, 0812.4002.
[14] O. Bohigas,et al. Fluctuation Properties of Nuclear Energy Levels and Widths : Comparison of Theory with Experiment , 1983 .
[15] Alan Edelman,et al. MOPS: Multivariate orthogonal polynomials (symbolically) , 2004, J. Symb. Comput..
[16] H. Frahm. Spectrum of a spin chain with inverse square exchange , 1993, cond-mat/9303050.
[17] J. Quastel,et al. Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions , 2010, 1003.0443.
[18] P. Forrester,et al. The Calogero-Sutherland Model and Generalized Classical Polynomials , 1996, solv-int/9608004.
[19] M. Rösler. Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators , 1998 .
[20] Luc Lapointe,et al. Exact operator solution of the Calogero-Sutherland model , 1995, q-alg/9509003.
[21] K. Takeuchi,et al. Growing interfaces uncover universal fluctuations behind scale invariance , 2011, Scientific reports.
[22] Yuan Xu,et al. Orthogonal Polynomials of Several Variables: Preface , 2001 .
[23] C. Dunkl. Symmetric functions and BN-invariant spherical harmonics , 2002, math/0207122.
[24] Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills , 2004, hep-th/0406093.
[25] Alan Edelman,et al. Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics , 2005 .
[26] Michael E. Fisher,et al. Walks, walls, wetting, and melting , 1984 .
[27] W. Fulton. Young Tableaux: With Applications to Representation Theory and Geometry , 1996 .
[28] Makoto Katori,et al. Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems , 2004 .
[29] Kurt Johansson. Discrete Polynuclear Growth and Determinantal Processes , 2003 .
[30] Francesco Calogero,et al. Solution of the One‐Dimensional N‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials , 1971 .
[31] K. Hikami. Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems , 1996 .
[32] J. Baik,et al. A model for the bus system in Cuernavaca (Mexico) , 2005, math/0510414.
[33] Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model , 1996, cond-mat/9609041.
[34] Lattice integrable systems of Haldane-Shastry type. , 1992, Physical review letters.
[35] P. A. P. Moran,et al. An introduction to probability theory , 1968 .
[36] A. González-López,et al. The Berry-Tabor conjecture for spin chains of Haldane-Shastry type , 2008, 0804.3685.
[37] Integrable spin chain with reflecting end , 1996, cond-mat/9602105.
[38] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1951 .
[39] H. Spohn,et al. One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality. , 2010, Physical review letters.
[40] P. Forrester. Log-Gases and Random Matrices (LMS-34) , 2010 .
[41] Rene F. Swarttouw,et al. Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.
[42] K. Johansson. Shape Fluctuations and Random Matrices , 1999, math/9903134.
[43] Scaling limit of vicious walks and two-matrix model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.
[44] T. Sasamoto,et al. Replica approach to the KPZ equation with the half Brownian motion initial condition , 2011, 1105.4659.
[45] P. Forrester,et al. Non-intersecting Brownian walkers and Yang–Mills theory on the sphere , 2010, 1009.2362.
[46] Polynuclear growth model with external source and random matrix model with deterministic source. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.
[47] Pandey,et al. Higher-order correlations in spectra of complex systems. , 1985, Physical review letters.
[48] P. G. de Gennes,et al. Soluble Model for Fibrous Structures with Steric Constraints , 1968 .
[49] G. Arfken. Mathematical Methods for Physicists , 1967 .
[50] M. Wadati,et al. Infinite Symmetry of the Spin Systems with Inverse Square Interactions , 1993 .
[51] Radial Dunkl processes: Existence, uniqueness and hitting time , 2009 .
[52] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .
[53] David J. Grabiner. Brownian Motion in a Weyl Chamber, Non-Colliding Particles, and Random Matrices , 1997, math/9708207.
[54] The Calogero-Sutherland model and polynomials with prescribed symmetry , 1996, solv-int/9609010.
[55] Spohn,et al. Universal distributions for growth processes in 1+1 dimensions and random matrices , 2000, Physical review letters.
[56] Charles F. Dunkl,et al. Integral Kernels with Reflection Group Invariance , 1991, Canadian Journal of Mathematics.
[57] R. Stanley. Some combinatorial properties of Jack symmetric functions , 1989 .
[58] Freeman J. Dyson,et al. The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics , 1962 .