The Annals of Applied Probability

Mesoscopic eigenvalue statistics of Wigner matrices

Yukun He and Antti Knowles

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Abstract

We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, that is, scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 3 (2017), 1510-1550.

Dates
Received: March 2016
First available in Project Euclid: 19 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1500451234

Digital Object Identifier
doi:10.1214/16-AAP1237

Mathematical Reviews number (MathSciNet)
MR3678478

Zentralblatt MATH identifier
1375.15055

Subjects
Primary: 15B52: Random matrices
Secondary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
Wigner matrices mesoscopic eigenvalue distribution linear statistics universality

Citation

He, Yukun; Knowles, Antti. Mesoscopic eigenvalue statistics of Wigner matrices. Ann. Appl. Probab. 27 (2017), no. 3, 1510--1550. doi:10.1214/16-AAP1237. https://projecteuclid.org/euclid.aoap/1500451234


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References

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