Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 46, 15 pp.
Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function
In , 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.
Electron. Commun. Probab., Volume 23 (2018), paper no. 46, 15 pp.
Received: 7 February 2018
Accepted: 18 July 2018
First available in Project Euclid: 27 July 2018
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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