Large N expansions for the Laguerre and Jacobi β-ensembles from the loop equations

DOI10.1063/1.4997778zbMath1384.82012arXiv1707.04842OpenAlexW3098089373MaRDI QIDQ4599465

Anas A. Rahman, Nicholas S. Witte, Peter J. Forrester

Publication date: 2 January 2018

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

Full work available at URL: https://arxiv.org/abs/1707.04842

zbMATH Keywords

random matrices\(\beta\)-ensemblesJacobi ensemblesLaguerre ensembles

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Transport processes in time-dependent statistical mechanics (82C70) Random matrices (algebraic aspects) (15B52) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

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High–low temperature dualities for the classical β-ensembles, Differential recurrences for the distribution of the trace of the \(\beta\)-Jacobi ensemble, Expanding the Fourier transform of the scaled circular Jacobi \(\beta\) ensemble density, Jacobi beta ensemble and \(b\)-Hurwitz numbers, \(\beta\)-ensembles and higher genera Catalan numbers, A review of exact results for fluctuation formulas in random matrix theory, Laguerre ensemble: correlators, Hurwitz numbers and Hodge integrals, Optimal soft edge scaling variables for the Gaussian and Laguerre even \(\beta\) ensembles, Symmetric function theory and unitary invariant ensembles, Beta Jacobi ensembles and associated Jacobi polynomials, Recursion for the smallest eigenvalue density of \(\beta \)-Wishart-Laguerre ensemble, Asymptotics of Hankel determinants with a Laguerre-type or Jacobi-type potential and Fisher-Hartwig singularities, Integer moments of complex Wishart matrices and Hurwitz numbers, Differential identities for the structure function of some random matrix ensembles, Moments of random matrices and hypergeometric orthogonal polynomials, Moments of discrete orthogonal polynomial ensembles, Relations between moments for the Jacobi and Cauchy random matrix ensembles, The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain, Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation, Linear differential equations for the resolvents of the classical matrix ensembles

Uses Software

• MOPS

Cites Work

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