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Universality for random matrix flows with time-dependent density.

Authors :
Erdős, László
Schnelli, Kevin
Source :
Annales de l'Institut Henri Poincare (B) Probability & Statistics. Nov2017, Vol. 53 Issue 4, p1606-1656. 51p.
Publication Year :
2017

Abstract

We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion of the eigenvalues hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from Wigner's semicircle law. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02460203
Volume :
53
Issue :
4
Database :
Academic Search Index
Journal :
Annales de l'Institut Henri Poincare (B) Probability & Statistics
Publication Type :
Academic Journal
Accession number :
126916953
Full Text :
https://doi.org/10.1214/16-AIHP765