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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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