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The local relaxation flow approach to universality of the local statistics for random matrices

László ErdősBenjamin SchleinHorng-Tzer YauJun Yin — 2012

Annales de l'I.H.P. Probabilités et statistiques

We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues { }=1 are close to their classical location { }=1 determined by the limiting density...

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