The Extremal Landscape of the C$\beta$E

Topic:
The Extremal Landscape of the C$\beta$E
Date & Time:
Tuesday, September 20, 2022 - 21:00 to 22:00
Speaker:
Ofer Zeitouni, Weizmann Institute of Science & Courant Institute, NYU
Location:
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).