Benedek Valko

The stochastic zeta function

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, the circular Jacobi ensemble and the truncated circular beta-ensemble.

Joint with Bálint Virág (Toronto) and Yun Li (Wisconsin).