Open Access
2016 Fluctuations of functions of Wigner matrices
László Erdős, Dominik Schröder
Electron. Commun. Probab. 21: 1-15 (2016). DOI: 10.1214/16-ECP38


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].


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László Erdős. Dominik Schröder. "Fluctuations of functions of Wigner matrices." Electron. Commun. Probab. 21 1 - 15, 2016.


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

zbMATH: 1355.60011
MathSciNet: MR3600514
Digital Object Identifier: 10.1214/16-ECP38

Primary: 15B52 , 60B20

Keywords: central limit theorem , Linear eigenvalue statistics , non-Gaussian fluctuation

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