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arXiv · 0810.0743

A connection between the Ghirlanda--Guerra identities and ultrametricity

Dmitry Panchenko
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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.

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Dmitry Panchenko. 2010-01-27. A connection between the Ghirlanda--Guerra identities and ultrametricity. https://doi.org/10.1214/09-aop484

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