Universality of Random Matrices and Local Relaxation Flow

Details Universality of Random Matrices and Local Relaxation Flow Universality of Random Matrices and Local Relaxation Flow

2009-07-31

arxiv.org/abs/0907.5605v5

Physics

Mathematical Physics

A minor error in the proof of Lemma 2.2 has been corrected and an additional technical condition was added to Cor. 2.4. Final

Scientific paper

We consider $N\times N$ symmetric random matrices where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove that the eigenvalue spacing statistics in the bulk of the spectrum for these matrices and for GOE are the same in the limit $N \to \infty$. Our approach is based on the study of the Dyson Brownian motion via a related new dynamics, the local relaxation flow.

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