  In Arguin & Tai (2018), 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.
