Exact results and universal asymptotics in the Laguerre random matrix ensemble

DOI10.1063/1.530883zbMath0807.60029OpenAlexW2078644713MaRDI QIDQ4314236

Peter J. Forrester

Publication date: 28 February 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530883

zbMATH Keywords

asymptotic formulasLaguerre random matrix ensemblegeneralized hypergeometric functions

Mathematics Subject Classification ID

Distribution theory (60E99)

Related Items

Application of the τ‐function theory of Painlevé equations to random matrices: P_V, P_III, the LUE, JUE, and CUE, Diffusion at the random matrix hard edge, Application of theτ-function theory of Painlevé equations to random matrices:P_VI, the JUE, CyUE, cJUE and scaled limits, On the Tracy-Widom\(_\beta\) distribution for \(\beta=6\), Applications and generalizations of Fisher–Hartwig asymptotics, Complex Wishart matrices and conductance in mesoscopic systems: Exact results, Hermite and Laguerre \(\beta\)-ensembles: asymptotic corrections to the eigenvalue density, The Bessel line ensemble, Rank 1 perturbations in random matrix theory — A review of exact results, Finite size corrections relating to distributions of the length of longest increasing subsequences, Smallest eigenvalue density for regular or fixed-trace complex Wishart–Laguerre ensemble and entanglement in coupled kicked tops, Asymptotic forms for hard and soft edge general \(\beta \) conditional gap probabilities, Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function, Asymptotics for products of characteristic polynomials in classical \(\beta\)-ensembles, Compact smallest eigenvalue expressions in Wishart–Laguerre ensembles with or without a fixed trace, Top eigenvalue of a random matrix: large deviations and third order phase transition, Limits for circular Jacobi beta-ensembles, The beta-Wishart ensemble, Recursion for the smallest eigenvalue density of \(\beta \)-Wishart-Laguerre ensemble, Universality of the stochastic Bessel operator, Random matrices: The distribution of the smallest singular values, The smallest eigenvalue distribution at the spectrum edge of random matrices, ASYMPTOTICS OF SPACING DISTRIBUTIONS AT THE HARD EDGE FOR β-ENSEMBLES, Linear differential equations for the resolvents of the classical matrix ensembles, Recursion scheme for the largest $\beta$ -Wishart–Laguerre eigenvalue and Landauer conductance in quantum transport, Schur expansion of random-matrix reproducing kernels

Cites Work

• Bessel functions of matrix argument
• The distribution and moments of the smallest eigenvalue of a random matrix of Wishart type
• Latent roots and matrix variates: a review of some asymptotic results
• Some combinatorial properties of Jack symmetric functions
• The spectrum edge of random matrix ensembles.
• Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
• Eigenvalues and Condition Numbers of Random Matrices
• A Class of Generalized Hypergeometric Functions in Several Variables
• Nonuniversal correlations for random matrix ensembles
• Laguerre ensembles of random matrices: Nonuniversal correlation functions
• An Asymptotic Expansion for the Noncentral Wishart Distribution