Universality classes for extreme-value statistics

The equilibrium low-temperature physics of disordered systems is governed by the statistics of extremely low-energy states. It is thus relevant to discuss the possible universality classes, for extreme-value statistics. We compare the usual probabilistic classification to the results of the replica approach. We show in detail for several problems (including the random energy model and the decaying Burgers turbulence) that one class of independent variables corresponds exactly to the so-called one step replica symmetry breaking solution in the replica language. We argue that this universality class holds if the correlations are sufficiently weak, and propose a conjecture on the level of correlations which leads to different universality classes.