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.
"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