Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function
[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.
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[效力级别] [学科分类] 统计和概率
[关键词] extreme value theory;Riemann zeta function;Ghirlanda-Guerra identities;Gibbs measure;Poisson-Dirichlet variable;ultrametricity;spin glasses [时效性]
