2011/12/31 by Dmitry Panchenko · 1 citation
Mathematics · #math.PR #msc:60K35 #msc:82B44
published as Ann. of Math. (2), Vol. 177, No. 1 (2013) 383-393 · arXiv admin note: text overlap with arXiv:1108.0379
arxiv created 2015/03/01 · arxiv updated 2015/03/03
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.