Open Access
2011 Random matrices: Universality of local eigenvalue statistics
Terence Tao, Van Vu
Author Affiliations +
Acta Math. 206(1): 127-204 (2011). DOI: 10.1007/s11511-011-0061-3


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.

Funding Statement

T. Tao is supported by a grant from the MacArthur Foundation, by NSF grant DMS-0649473, and by the NSF Waterman award.
V. Vu is supported by research grants DMS-0901216 and AFOSAR-FA-9550-09-1-0167.


Download Citation

Terence Tao. Van Vu. "Random matrices: Universality of local eigenvalue statistics." Acta Math. 206 (1) 127 - 204, 2011.


Received: 8 June 2009; Published: 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1217.15043
MathSciNet: MR2784665
Digital Object Identifier: 10.1007/s11511-011-0061-3

Primary: 15A52

Rights: 2011 © Institut Mittag-Leffler

Vol.206 • No. 1 • 2011
Back to Top