Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case

Dmitry Panchenko

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arXiv · 1106.3984

Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case

Dmitry Panchenko

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Abstract

In this paper 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 Dobvysh-Sudakov representation, is based only on elementary algebraic consequences of the Ghirlanda-Guerra identities.

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Dmitry Panchenko. 2011-06-20. Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case. https://arxiv.org/abs/1106.3984

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