高温下混合 p-自旋模型的谱隙估计值

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY Probability Theory and Related Fields Pub Date : 2024-03-17 DOI:10.1007/s00440-024-01261-9

Arka Adhikari, Christian Brennecke, Changji Xu, Horng-Tzer Yau

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引用次数: 0

摘要

我们考虑了一般的混合 p-自旋均场自旋玻璃模型，并提供了一种方法来证明在足够高的温度下，与吉布斯量相关的 Dirichlet 形式的谱间隙是一阶的。我们的证明基于一个迭代方案，它将 N-自旋系统的谱间隙与适当条件的子系统的谱间隙联系起来。

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Spectral gap estimates for mixed p-spin models at high temperature

We consider general mixed p-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based on an iteration scheme relating the spectral gap of the N-spin system to that of suitably conditioned subsystems.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.