Covariance kernel of linear spectral statistics for half-heavy tailed wigner matrices

In this paper, we analyze the covariance kernel of Gaussian process that arises as limit fluctuations linear spectral statistics for Wigner matrices with a few moments. More precisely, study here corresponds to Hermitian independent entries have [Formula: see text] moments text]. We obtain closed form text]-dependent expression limiting resulting from Stieltjes transform by explicitly integrating known double Laplace integral formula obtained in [F. Benaych-Georges and A. Maltsev, Fluctuations half-heavy-tailed random matrices, Stochastic Process. Appl. 126(11) (2016) 3331–3352]. then express an acting on bounded continuous test functions. The formulation allows us offer heuristic interpretation impact typical large eigenvalues matrix ensemble structure.