Application of the τ‐function theory of Painlevé equations to random matrices: PV, PIII, the LUE, JUE, and CUE

DOI10.1002/cpa.3021zbMath1029.34087arXivmath-ph/0201051OpenAlexW2074380165MaRDI QIDQ4790303

Nicholas S. Witte, Peter J. Forrester

Publication date: 28 January 2003

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0201051

zbMATH Keywords

random matricesinteracting random processesPainlevé equationsreflection groups

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

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Multiple phases and meromorphic deformations of unitary matrix models, Classical solutions of the degenerate fifth Painlevé equation, Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues, Large \(z\) asymptotics for special function solutions of Painlevé II in the complex plane, Painlevé V and the Hankel determinant for a singularly perturbed Jacobi weight, Joint moments of a characteristic polynomial and its derivative for the circular \(\beta \)-ensemble, Discrete Painlevé system for the partition function of N _f  =  2 SU(2) supersymmetric gauge theory and its double scaling limit, Painlevé III Asymptotics of Hankel Determinants for a Perturbed Jacobi Weight, Moduli spaces of \(d\)-connections and difference Painlevé equations, Application of theτ-function theory of Painlevé equations to random matrices:P_VI, the JUE, CyUE, cJUE and scaled limits, Center of mass distribution of the Jacobi unitary ensembles: Painlevé V, asymptotic expansions, Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE, Special function solutions of Painlevé equations: theory, asymptotics and applications, Factorization of correlation functions and the replica limit of the Toda lattice equation, Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations, On a distinguished family of random variables and Painlevé equations, Truncated Hermite polynomials, Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlevé V system, Integrable differential systems for deformed Laguerre–Hahn orthogonal polynomials, Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble, On linear systems and \(\tau\) functions associated with Lamé's equation and Painlevé's equation VI, Exact solution of interacting particle systems related to random matrices, Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system, Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions, Toeplitz determinants with merging singularities, Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach, Discrete gap probabilities and discrete Painlevé equations., Transmutation of a trans-series: the Gross-Witten-Wadia phase transition, Singular Values of Products of Ginibre Random Matrices, Linear systems, Hankel products and the sinh-Gordon equation, On the Lax Pairs of the Symmetric Painlevé Equations, Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory, Similarity reductions of peakon equations: the $b$-family, Largest Schmidt eigenvalue of random pure states and conductance distribution in chaotic cavities, Painlevé III' and the Hankel determinant generated by a singularly perturbed Gaussian weight, Integrable structure of products of finite complex Ginibre random matrices, Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter, Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I., A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions, Crossing bridges with strong Szegő limit theorem, How much can the eigenvalues of a random Hermitian matrix fluctuate?, A matrix model with a singular weight and Painlevé III, τ-function of discrete isomonodromy transformations and probability, Painlevé IV: A numerical study of the fundamental domain and beyond, Gap probability for products of random matrices in the critical regime, Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions, The generalized Krawtchouk polynomials and the fifth Painlevé equation, Expectations of hook products on large partitions and the chi-square distribution, Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation, Integrable aspects of universal quantum transport in chaotic cavities, Matrix models for classical groups and Toeplitz ± Hankel minors with applications to Chern–Simons theory and fermionic models

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