The generalised Dyson circular unitary ensemble: asymptotic distribution of the eigenvalues at the origin of the spectrum
type: Item
instance of: scholarly article
title: The generalised Dyson circular unitary ensemble: asymptotic distribution of the eigenvalues at the origin of the spectrum
zbMATH Open document ID: 1217.15042
author: Philippe Rambour
author: Abdellatif Seghier
published in: Integral Equations and Operator Theory
publication date: 2011-05-25T00:00:00Z
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 5899576
zbMATH Keywords: random unitary matrices
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Fisher-Hartwig conjecture
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: Christoffel-Darboux kernel
zbMATH Keywords: distribution of eigenvalues
zbMATH Keywords: Toeplitz matrix
MaRDI profile type: Publication
full work available at URL: s00020-010-1853-0
OpenAlex ID: W2162998084
cites work: Asymptotic Formulas for Toeplitz Determinants
cites work: Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
cites work: The Onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators.
cites work: Toeplitz matrices and determinants with Fisher-Hartwig symbols
cites work: Toeplitz Operators and Determinants Generated by Symbols with One Fisher-Hartwig Singularity
cites work: New results on the equilibrium measure for logarithmic potentials in the presence of an external field
cites work: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach.
cites work: A Brownian-Motion Model for the Eigenvalues of a Random Matrix
cites work: Statistical Theory of the Energy Levels of Complex Systems. I
cites work: The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics
cites work: Applications and generalizations of Fisher–Hartwig asymptotics
cites work: On random matrices from the compact classical groups
cites work: Traces and determinants of linear operators
cites work: Universality for eigenvalue correlations at the origin of the spectrum
cites work: Maximum entropy and the moment problem
cites work: Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
cites work: Szegő orthogonal polynomials with respect to an analytic weight: Canonical representation and strong asymptotics
cites work: Impact of localization on Dyson's circular ensemble
cites work: Asymptotic inverse of Toeplitz matrices with symbol \((1-\cos \theta )^\alpha f_1\), \(\frac{-1}{2} <\alpha \leq\frac12\), and integral kernels
cites work: Inversion of Toeplitz matrices whose symbols admit a root of positive rational order for the minimal eigenvalue.
cites work: Q4185363
cites work: Level-spacing distributions and the Airy kernel
cites work: Correlation functions, cluster functions, and spacing distributions for random matrices
cites work: Universality of the distribution functions of random matrix theory
cites work: Q4435456
DOI: 10.1007/S00020-010-1853-0
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description: scientific article; zbMATH DE number 5899576