The Parisi ultrametricity conjecture
Probability
2015-03-03 v2
Abstract
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 -spin models, for which Gibbs' measures are known to satisfy the Ghirlanda-Guerra identities in the thermodynamic limit.
Keywords
Cite
@article{arxiv.1112.1003,
title = {The Parisi ultrametricity conjecture},
author = {Dmitry Panchenko},
journal= {arXiv preprint arXiv:1112.1003},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1108.0379