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arXiv · 1112.1003

The Parisi ultrametricity conjecture

Dmitry Panchenko
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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 $p$-spin models, for which Gibbs' measures are known to satisfy the Ghirlanda-Guerra identities in the thermodynamic limit.

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Dmitry Panchenko. 2015-03-01. The Parisi ultrametricity conjecture. https://arxiv.org/abs/1112.1003

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