Electronic Communications in Probability

Fluctuations of functions of Wigner matrices

László Erdős and Dominik Schröder

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Abstract

We show that matrix elements of functions of $N\times N$ Wigner matrices fluctuate on a scale of order $N^{-1/2}$ and we identify the limiting fluctuation. Our result holds for any function $f$ of the matrix that has bounded variation thus considerably relaxing the regularity requirement imposed in [7, 11].

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 86, 15 pp.

Dates
Received: 31 October 2016
Accepted: 13 December 2016
First available in Project Euclid: 2 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1483347665

Digital Object Identifier
doi:10.1214/16-ECP38

Mathematical Reviews number (MathSciNet)
MR3600514

Zentralblatt MATH identifier
1355.60011

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

Keywords
linear eigenvalue statistics central limit theorem non-Gaussian fluctuation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Erdős, László; Schröder, Dominik. Fluctuations of functions of Wigner matrices. Electron. Commun. Probab. 21 (2016), paper no. 86, 15 pp. doi:10.1214/16-ECP38. https://projecteuclid.org/euclid.ecp/1483347665


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References

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