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

Electronic Communications in Probability

Frédéric Ouimet¹ 

关键词: extreme value theory;    Riemann zeta function;    Ghirlanda-Guerra identities;    Gibbs measure;    Poisson-Dirichlet variable;    ultrametricity;    spin glasses;   

DOI  :  10.1214/18-ECP154

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

In [4], 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.

【 授权许可】

CC BY