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arXiv:0810.0743 [math.PR]AbstractReferencesReviewsResources

A connection between the Ghirlanda--Guerra identities and ultrametricity

Dmitry Panchenko

Published 2008-10-04, updated 2010-01-27Version 4

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.

Comments: Published in at http://dx.doi.org/10.1214/09-AOP484 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2010, Vol. 38, No. 1, 327-347
Categories: math.PR, math-ph, math.MP
Subjects: 60K35, 82B44
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