Ghirlanda-Guerra identities and ultrametricity: An elementary proof in   the discrete case
  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. 
Dmitry Panchenko
math.PR math-ph math.MP