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The low temperature physics of disordered systems is governed by thestatistics of extremely low energy states. It is thus rather important todiscuss the possible universality classes for extreme value statistics. Wecompare the usual probabilistic classification to the results of the replicaapproach. We show in detail that one class of independent variables correspondsexactly to the so-called one step replica symmetry breaking solution in thereplica language. This universality class holds if the correlations aresufficiently weak. We discuss the relation between the statistics of extremesand the problem of Burgers turbulence in decay.Comment: LateX, 20 pages, 2 postscript figures, submitted to J. Phys.

Universality classes for extreme-value statistics