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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

Abstract

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.

Citation

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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. https://doi.org/10.1214/18-ECP154

Information

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

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

JOURNAL ARTICLE
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