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Universality for Random Matrix Flows with Time-dependent Density
Published 2 Apr 2015 in math.PR, math-ph, and math.MP | (1504.00650v2)
Abstract: We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion 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 the Wigner semicircle law.
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