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Dominik Schröder

Fluctuations of functions of Wigner matrices

László Erdős, Dominik Schröder

Electron. Commun. Probab.Vol. 21 (2016)


We prove a CLT for the entrywise fluctuations of functions of random matrices. The use of Pleijel's formula makes our result applicable to all functions of bounded variation.


We show that matrix elements of functions of N×NN\times N Wigner matrices fluctuate on a scale of order N1/2N^{-1/2} and we identify the limiting fluctuation. Our result holds for any function ff of the matrix that has bounded variation and thus considerably relaxes the regularity requirement imposed in [7,11].