A connection between the Ghirlanda–Guerra identities and ultrametricity

A connection between the Ghirlanda–Guerra identities and ultrametricity

Dmitry Panchenko

Source: Ann. Probab. Volume 38, Number 1 (2010), 327-347.

Abstract

We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda–Guerra identities imply ultrametricity.

First Page: Show

Primary Subjects: 60K35, 82B44

Keywords: Sherrington–Kirkpatrick model; Parisi ultrametricity conjecture

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1264434001
Digital Object Identifier: doi:10.1214/09-AOP484
Mathematical Reviews number (MathSciNet): MR2599202
Zentralblatt MATH identifier: 1196.60167

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