Open Collections

Description

We give a proof that the maximum of the centered log-potential of GUE is log N + o(log N) with high probability. This confirms the first term in a conjecture by Fyodorov and Simm. Moreover, we prove a general theorem about almost Gaussian fields that should be applicable to showing the law of large numbers for the log characteristic polynomial of beta-ensembles. We will also survey some extensions of this type of result: to other potentials, to other beta, and to higher degrees of precision. This is based on joint works with Gaultier Lambert and Ofer Zeitouni.