A new representation of the Ghirlanda-Guerra identities with applications

2011/08/01 by Dmitry Panchenko, Panchenko, Dmitry · 1 citation
Mathematics · #60K35 #82B44 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K35 #msc:82B44

paper · pdf · doi:10.48550/arxiv.1108.0379

arxiv created 2011/11/29 · arxiv updated 2011/11/30

Abstract

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.

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