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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)
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