A new representation of the Ghirlanda-Guerra identities with applications

Dmitry Panchenko

Published 2011-08-01, updated 2011-11-29Version 2

In this paper we obtain a new family of identities for random measures on the unit ball of a separable Hilbert space which arise as the asymptotic analogues of the Gibbs measures in the Sherrington-Kirkpatrick and $p$-spin models and which are known to satisfy the Ghirlanda-Guerra identities. We give several applications of the new identities to structural results for such measures.