A new representation of the Ghirlanda-Guerra identities with applications

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.

References in corpus (2)

• A unified stability property in spin glasses
• Random Overlap Structures: Properties and Applications to Spin Glasses

Cited by in corpus (1)

• On the Mixed Even-Spin Sherrington-Kirkpatrick Model with Ferromagnetic Interaction