Universality Of The Local Eigenvalue Statistics For A Class Of Unitary Invariant Random Matrix Ensembles

Universality Of The Local Eigenvalue Statistics For A Class Of Unitary Invariant Random Matrix Ensembles (1997)

by L. Pastur , M. Shcherbina

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Datum	Value	Source
TITLE	Universality Of The Local Eigenvalue Statistics For A Class Of Unitary Invariant Random Matrix Ensembles	user correction - Legacy Corrections
AUTHOR NAME	L. Pastur	user correction - Legacy Corrections
AUTHOR NAME	M. Shcherbina	user correction - Legacy Corrections
ABSTRACT	The paper is devoted to the rigorous proof of the universality conjecture of the random matrix theory, according to which the limiting eigenvalue statistics of n \Theta n random matrices within spectral intervals of the order O(n \Gamma1 ) is determined by the type of matrices (real symmetric, Hermitian or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arose in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions. Key words: random matrices, local asymptotic regime, universality conjecture, orthogonal polynomial technique. 1 Introduction. Problem and results. The random matrix theory (RMT) has been extensively developed and used in a number of areas of theoretical and mathematical physics. In particular the theory provides quite satisfactory description of fluctuations in s...	user correction - Legacy Corrections
YEAR	1997	user correction - Legacy Corrections
CITATIONS	18 found	ParsCit 1.0