## CLT for linear spectral statistics of Wigner matrices.(English)Zbl 1188.15032

Summary: We prove that the spectral empirical process of Wigner matrices under sixth-moment conditions, which is indexed by a set of functions with continuous fourth-order derivatives on an open interval including the support of the semicircle law, converges weakly in finite dimensions to a Gaussian process.

### MSC:

 15B52 Random matrices (algebraic aspects) 60F05 Central limit and other weak theorems 60G15 Gaussian processes
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