Approximate Ultrametricity for Random Measures and Applications to Spin Glasses
Approximate Ultrametricity for Random Measures and Applications to Spin Glasses
复制标题
随机测量的近似超量度及其在旋转玻璃中的应用
DOI：
10.1002/cpa.21685
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发表时间：
2014
影响因子：
3
通讯作者：
Aukosh Jagannath
中科院分区：
文献类型：
--
作者：
Aukosh Jagannath
在本文中，我们引入了一个称为“近似超度量”的概念，它封装了一系列随机概率度量的现象学，这些随机概率度量的支撑点在分解成嵌套球的情况下表现为超度量空间。我们给出了无限维可分Hilbert空间单位球上的随机概率测度序列允许这种分解的一个充分条件，其元素称为簇。我们还刻画了簇的度量的定律，证明了它们在法律上收敛到Ruelle概率级联的权重。这些结果适用于平均场自旋玻璃中的一大类经典模型。我们通过证明TALAGRAND关于混合p自旋玻璃的猜想来说明近似超度规的概念，该猜想暗示了Dotsenko-Franz-Mézard的预测。©2017威利期刊公司。
In this documentname, 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 a conjecture of Talagrand regarding mixed p‐spin glasses that is known to imply a prediction of Dotsenko‐Franz‐Mézard. © 2017 Wiley Periodicals, Inc.
自旋玻璃的对偶原理
影响因子：
1.4
作者：
Auffinger, Antonio;Chen, Wei-Kuo
通讯作者：
Chen, Wei-Kuo