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arXiv:1112.1003 [math.PR]AbstractReferencesReviewsResources

The Parisi ultrametricity conjecture

Dmitry Panchenko

Published 2011-12-05, updated 2015-03-01Version 2

In this paper we prove that the support of a random measure on the unit ball of a separable Hilbert space that satisfies the Ghirlanda-Guerra identities must be ultrametric with probability one. This implies the Parisi ultrametricity conjecture in mean-field spin glass models, such as the Sherrington-Kirkpatrick and mixed $p$-spin models, for which Gibbs' measures are known to satisfy the Ghirlanda-Guerra identities in the thermodynamic limit.

Comments: arXiv admin note: text overlap with arXiv:1108.0379
Journal: Ann. of Math. (2), Vol. 177, No. 1 (2013) 383-393
Categories: math.PR
Subjects: 60K35, 82B44
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