A connection between the Ghirlanda--Guerra identities and ultrametricity

Details A connection between the Ghirlanda--Guerra identities and ultrametricity A connection between the Ghirlanda--Guerra identities and ultrametricity

2008-10-04

arxiv.org/abs/0810.0743v4

Annals of Probability 2010, Vol. 38, No. 1, 327-347

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AOP484 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP484

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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