Asymptotic spectral independence of Wigner ensembles

Details Asymptotic spectral independence of Wigner ensembles Asymptotic spectral independence of Wigner ensembles

2011-10-04

arxiv.org/abs/1110.0810v1

Mathematics

Probability

Scientific paper

We consider the joint distribution of eigenvalue clusters of the Wigner ensemble separated by macroscopic distances (i.e., on the same scale as the difference between the edges of the semicircle law). We prove that under an averaging condition, the correlation function governing any finite collection of clusters converges to that of independence point processes. The proof relies heavily on the machinery developed by Erdos, Ramirez, Schlein, and Yau.

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