Open Access
2018 Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function
Frédéric Ouimet
Electron. Commun. Probab. 23: 1-15 (2018). DOI: 10.1214/18-ECP154


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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Frédéric Ouimet. "Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function." Electron. Commun. Probab. 23 1 - 15, 2018.


Received: 7 February 2018; Accepted: 18 July 2018; Published: 2018
First available in Project Euclid: 27 July 2018

zbMATH: 06924035
MathSciNet: MR3841407
Digital Object Identifier: 10.1214/18-ECP154

Primary: 11M06 , 60F05 , 60G60 , 60G70

Keywords: Extreme value theory , Ghirlanda-Guerra identities , Gibbs measure , Poisson-Dirichlet variable , Riemann zeta function , Spin glasses , Ultrametricity

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