Benedek Valkó -- The stochastic zeta function
Channel: Matrices Et Graphes Aléatoires GDR CNRS
Date: 2021-02-15

Abstract : Chhaibi, Najnudel and Nikhekgbali introduced a random entire function with zero set given by the points of the Sine_2 process, the point process limit of the circular unitary ensemble (CUE). They showed that the function is the limit of the normalized characteristic polynomials of the CUE. We provide new descriptions for this random function: as a power series built from Brownian motion, as a determinant connected to a random differential operator, and as the stationary solution of an SDE. Our approach extends to various generalizations of the CUE: the circular beta-ensemble, and the Hua-Pickrell ensemble.
Joint with B. Virág (Toronto) and Yun Li (Wisconsin).