Speaker: Fanny Augeri
Affiliation: Weizmann Institute of Science
In this talk, I will be concerned by the problem of the large deviations of the spectrum of Wigner matrices. More precisely, I will focus on understanding the deviations of macroscopic statistics of the spectrum like the empirical distribution of the eigenvalues, the largest eigenvalue and traces of powers. I will present some large deviations principles for a class of Wigner matrices called “without Gaussian tails” for which the large deviations of its spectrum are governed by a heavy-tail phenomenon, meaning that only a small proportion of the entries of the matrix participate in the deviations. In a first part of the talk, I will present some concentration inequalities for macroscopic statistics of the spectrum for Wigner matrices having weaker concentration properties that normal concentration. Then in a second part, I will explain the strategy developed to exploit this heavy-tail phenomenon appearing in the large deviations of Wigner matrices “without Gaussian tails” so as to obtain full large deviations principles.