We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$\beta$E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) towards the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a "derivative martingale''. We also provide a description of the landscape near extrema points. (Joint work with Elliot Paquette).
Ofer Zeitouni got his PhD in Electrical Engineering from the Technion, Israel in 1986. After a post-doc at Brown University and MIT, he has been on the faculty of the Technion (1989-2006), the University of Minnesota (2002-2012), and, since 2007, the Weizmann Institute. He is also a global distinguished professor of Mathematics at the Courant Institute, NYU. Zeitouni's research interests are in probability theory, with recent focus on extremes of logarithmically correlated fields, random matrices, and motion in random media.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai