Fluctuations of linear statistics of half-heavy-tailed random matrices

Florent Benaych-Georges, Anna Maltsev

We consider a Wigner matrix $A$ with entries tail decaying as $x^{-\alpha }$ with $2<\alpha <4$ for large $x$ and study fluctuations of linear statistics $N^{-1}\mathrm{Tr}\phi (A)$. The beh…