Comptes Rendus
Probability Theory/Mathematical Physics
Ghirlanda–Guerra identities and ultrametricity: An elementary proof in the discrete case
Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 813-816.

In this Note we give another proof of the fact that a random overlap array, which satisfies the Ghirlanda–Guerra identities and whose elements take values in a finite set, is ultrametric with probability one. The new proof bypasses random change of density invariance principles for directing measures of such arrays and, in addition to the Dovbysh–Sudakov representation, is based only on elementary algebraic consequences of the Ghirlanda–Guerra identities.

Dans cette Note nous donnons une nouvelle preuve du fait quʼune matrice aléatoire infinie, qui satisfait lʼidentité Ghirlanda–Guerra et dont les coefficiants prennent leurs valeurs dans un ensemble fini, est ultramétrique avec probabilité un. La preuve utilise uniquement des conséquences algébriques élémentaires des identités Ghirlanda–Guerra et la représentation de Dovbysh–Sudakov.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.06.021
Dmitry Panchenko 1

1 Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA
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Dmitry Panchenko. Ghirlanda–Guerra identities and ultrametricity: An elementary proof in the discrete case. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 813-816. doi : 10.1016/j.crma.2011.06.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.021/

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