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)