Geodesic
The Parisi ultrametricity conjecture
Dmitry Panchenko1
1 Department of Mathematics, Texas A&M University, College Station, TX 77843
Annals of mathematics, Tome 177 (2013) no. 1, pp. 383-393.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2013.177.1.8

Dmitry Panchenko 1

1 Department of Mathematics, Texas A&M University, College Station, TX 77843 
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Dmitry Panchenko. The Parisi ultrametricity conjecture. Annals of mathematics, Tome 177 (2013) no. 1, pp. 383-393. doi : 10.4007/annals.2013.177.1.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.1.8/

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