2009

Random matrices: Universality of local eigenvalue statistics

Tao, Terence, Vu, Van

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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.

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