Parisi PDE and convexity for vector spins

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-07-21 DOI:10.1016/j.spa.2025.104746

Hong-Bin Chen

引用次数: 0

Abstract

We consider mean-field vector spin glasses with self-overlap correction. The limit of free energy is known to be the Parisi formula, which is an infimum over matrix-valued paths. We decompose such a path into a Lipschitz matrix-valued path and the quantile function of a one-dimensional probability measure. For such a pair, we associate a Parisi PDE generalized for vector spins. Under mild conditions, we rewrite the Parisi formula in terms of solutions of the PDE. Moreover, for each fixed Lipschitz path, the Parisi functional is strictly convex over probability measures.

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向量自旋的Parisi PDE和凸性

我们考虑具有自重叠校正的平均场矢量自旋玻璃。自由能的极限是已知的Parisi公式，它是矩阵值路径上的最小值。我们将这样的路径分解为一个利普希茨矩阵值路径和一个一维概率测度的分位数函数。对于这样的一对，我们关联了一个广义的Parisi PDE。在温和条件下，我们用PDE的解重写了Parisi公式。此外，对于每个固定的Lipschitz路径，Parisi泛函在概率测度上是严格凸的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.