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January 2010 A connection between the Ghirlanda–Guerra identities and ultrametricity
Dmitry Panchenko
Ann. Probab. 38(1): 327-347 (January 2010). DOI: 10.1214/09-AOP484

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.

Citation

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Dmitry Panchenko. "A connection between the Ghirlanda–Guerra identities and ultrametricity." Ann. Probab. 38 (1) 327 - 347, January 2010. https://doi.org/10.1214/09-AOP484

Information

Published: January 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1196.60167
MathSciNet: MR2599202
Digital Object Identifier: 10.1214/09-AOP484

Subjects:
Primary: 60K35, 82B44

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 1 • January 2010
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