随机交换模型的谱隙

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-09-12 DOI:10.1016/j.spa.2025.104769

Eric A. Carlen , Gustavo Posta , Imre Péter Tóth

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引用次数: 0

摘要

我们证明了Gaspard和Gilbert以及Grigo， Khanin和Szász研究的随机交换模型的谱间隙不等式，并与理解确定性台球模型中的热传导有关。我们所证明的谱隙的界在粒子数上是一致的，正如我们所推测的那样。我们采用了最初开发的技术来证明具有硬球碰撞的Kac模型的谱间隙界限，硬球碰撞与随机交换模型一样，具有退化跳变率。

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Spectral gap for the stochastic exchange model

We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Szász in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates.

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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.