English

A connection between the Ghirlanda--Guerra identities and ultrametricity

Probability 2010-01-27 v4 Mathematical Physics math.MP

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.

Cite

@article{arxiv.0810.0743,
  title  = {A connection between the Ghirlanda--Guerra identities and ultrametricity},
  author = {Dmitry Panchenko},
  journal= {arXiv preprint arXiv:0810.0743},
  year   = {2010}
}

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)

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