Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case
Probability
2011-07-29 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1106.3984,
title = {Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case},
author = {Dmitry Panchenko},
journal= {arXiv preprint arXiv:1106.3984},
year = {2011}
}