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

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

2011-06-20

arxiv.org/abs/1106.3984v1

C. R. Acad. Sci. Paris, Ser. I {349} (2011) 813-816

Mathematics

Probability

Scientific paper

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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