Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function

Abstract

In Arguin & Tai (2018), the authors prove the convergence of the two-overlap distribution at low temperature for a randomized Riemann zeta function on the critical line. We extend their results to prove the Ghirlanda-Guerra identities. As a consequence, we find the joint law of the overlaps under the limiting mean Gibbs measure in terms of Poisson-Dirichlet variables. It is expected that we can adapt the approach to prove the same result for the Riemann zeta function itself.

15 pages, 1 figure

Cited by in corpus (2)

• Moments of the Riemann zeta function on short intervals of the critical line
• Large deviations and continuity estimates for the derivative of a random model of $\log |\zeta |$ on the critical line