## Electronic Communications in Probability

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

Frédéric Ouimet

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 46, 15 pp.

Dates
Accepted: 18 July 2018
First available in Project Euclid: 27 July 2018

https://projecteuclid.org/euclid.ecp/1532657018

Digital Object Identifier
doi:10.1214/18-ECP154

Mathematical Reviews number (MathSciNet)
MR3841407

Zentralblatt MATH identifier
06924035

#### Citation

Ouimet, Frédéric. Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function. Electron. Commun. Probab. 23 (2018), paper no. 46, 15 pp. doi:10.1214/18-ECP154. https://projecteuclid.org/euclid.ecp/1532657018

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