Terence Tao, Van Vu
Published 2009-06-02, updated 2010-06-29Version 10
In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the distribution of the entries. As a consequence, we derive the universality of eigenvalue gap distribution and $k$-point correlation and many other statistics (under some mild assumptions) for both Wigner Hermitian matrices and Wigner real symmetric matrices.
Comments: 67 pages; to appear, Acta Math. Some additional corrections and references
On the universality of the probability distribution of the product $B^{-1}X$ of random matrices
Random matrices: Universality of ESDs and the circular law
Universality of local eigenvalue statistics in random matrices with external source
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