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arXiv · 1610.07084

Fluctuations of Functions of Wigner Matrices

László Erdős·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 and thus considerably relaxes the regularity requirement imposed in [7,11].

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László Erdős, Dominik Schröder. 2016-10-22. Fluctuations of Functions of Wigner Matrices. https://doi.org/10.1214/16-ecp38

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