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arXiv:0906.0510math.PR

Random matrices: Universality of local eigenvalue statistics

Terence Tao, Van Vu

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Abstract

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.

arXiv comments
67 pages; to appear, Acta Math. Some additional corrections and references
Journal reference
DOI
Subjects
math.PRProbability

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  1. The Universal Pattern Popping Up in Math, Physics and Biology (2013) 1 comment

    • I'm going to go out on a limb and say you posted this accidentally on the wrong thread somehow, but this isn't (at all) a theory of everything, nor is it some crank producing anything. Eg https://arxiv.org/abs/0906.0510 See the authors- in terms of contemporary mathematics they…

      seanhunterView on HNParent context

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