



























In this paper, we introduce a notion called "Approximate Ultrametricity" which encapsulates the phenomenology of a sequence of random probability measures having supports that behave like ultrametric spaces insofar as they decompose into nested balls. We provide a sufficient condition for a sequence of random probability measures on the unit ball of an infinite dimensional separable Hilbert space to admit such a decomposition, whose elements we call clusters. We also characterize the laws of the measures of the clusters by showing that they converge in law to the weights of a Ruelle Probability Cascade. These results apply to a large class of classical models in mean field spin glasses. We illustrate the notion of approximate ultrametricity by proving two important conjectures regarding mixed p-spin glasses.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。