Asymptotic corrections to the eigenvalue density of the GUE and LUE

DOI10.1063/1.2035028zbMath1111.82020arXivmath-ph/0504053OpenAlexW2035876291MaRDI QIDQ3438633

Timothy M. Garoni, N. E. Frankel, Peter J. Forrester

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/math-ph/0504053

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

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Moments of the Gaussian β ensembles and the large-N expansion of the densities, Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE, Hermite and Laguerre \(\beta\)-ensembles: asymptotic corrections to the eigenvalue density, Large N expansions for the Laguerre and Jacobi β-ensembles from the loop equations, Almost-Hermitian random matrices and bandlimited point processes, Some recent methods for establishing universality limits, Optimal soft edge scaling variables for the Gaussian and Laguerre even \(\beta\) ensembles, Edgeworth expansion of the largest eigenvalue distribution function of Gaussian unitary ensemble revisited, Universality limits in the bulk for varying measures, Density of states for Gaussian unitary ensemble, Gaussian orthogonal ensemble, and interpolating ensembles through supersymmetric approach, Fixed trace β-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density, Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble, Linear differential equations for the resolvents of the classical matrix ensembles, Asymptotic form of the density profile for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry, Raney distributions and random matrix theory

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