The Parisi ultrametricity conjecture

Details The Parisi ultrametricity conjecture The Parisi ultrametricity conjecture

2011-12-05

arxiv.org/abs/1112.1003v1

Mathematics

Probability

Scientific paper

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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