Bálint Virág: The stochastic zeta function

Speaker: Bálint Virág

Title: The stochastic zeta function

Abstract: Just like in sparse graph limit theory, one can take a statistical limit of deterministic analytic functions by re-centering them at a well-chosen a random point. EE What should we expect the limit of the Riemann zeta function to be? EE The conjectured answer comes from random matrix theory. We construct a random operator in the de Branges theory of canonical systems whose eigenvalues are conjectured to be random limit of the zeta zeros. It is based on Brownian motion in the Bolyai hyperbolic plane. EE The theory provides an analytic function related to this operator, an analogue of characteristic polynomials for matrices.  We call it the stochastic zeta function. EE Joint work with Benedek Valko.