## Fluctuations of functions of Wigner matrices.(English)Zbl 1355.60011

Summary: 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 [A. Lytova, Zh. Mat. Fiz. Anal. Geom. 9, No. 4, 536–581 (2013; Zbl 1296.60058); S. O’Rourke et al., J. Theor. Probab. 26, No. 3, 750–780 (2013; Zbl 1280.15021)].

### MSC:

 60B20 Random matrices (probabilistic aspects) 15B52 Random matrices (algebraic aspects)

### Citations:

Zbl 1296.60058; Zbl 1280.15021
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