Large deviations for the largest eigenvalue of sub-Gaussian matrices

Fanny Augeri, Alice Guionnet, Jonathan Husson

Published 2019-11-24Version 1

We establish large deviations estimates for the largest eigenvalue of Wigner matrices with sub-Gaussian entries. We estimate the probability that the largest eigenvalue is close to some value large enough and show that if the entries do not have sharp sub-Gaussian tails, the rate function is strictly smaller than the rate function for Gaussian entries. This contrasts with \cite{HuGu} where it was shown that the law of the largest eigenvalue of Wigner matrices with entries with sharp sub-Gaussian tails obeys a large deviation principle with the same rate function than in the Gaussian case.