Universality for random matrix flows with time dependent density

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

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IST Austria: PubRep (Institute of Science and Technology)

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Last time updated on 15/12/2019

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