A new representation of the Ghirlanda-Guerra identities with applications

TL;DR

This paper introduces a new family of identities for random measures related to spin glass models, providing novel insights and applications to their structural properties.

Contribution

It presents a novel formulation of the Ghirlanda-Guerra identities with applications to understanding the structure of measures in spin glass models.

Findings

New identities for random measures on Hilbert spaces.

Applications to structural analysis of Gibbs measures.

Enhanced understanding of spin glass measure properties.

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.