Séminaire de Probabilités commun ICJ/UMPA

# Large deviation estimate for the largest eigenvalue of a random matrix.

## by Raphael Ducatez

Europe/Paris
ICJ - bâtiment Braconnier - salle Fokko du Cloux

#### ICJ - bâtiment Braconnier - salle Fokko du Cloux

Description

We compute large deviation estimates of probability for the largest eigenvalue of a Wigner matrix with sub-Gaussian entries. We improve the results from the work of F.Augeri, A Guionnet, J Husson. to obtain an estimate valid on the whole real line. The main tools here is the matrix and spherical integral that plays a similar role as a Laplace transform.