具有无界单调率的平均场零范围过程:混合时间、截止时间和庞卡罗常数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-04-21 DOI:10.1214/22-aap1851

Hong-Quan Tran

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引用次数: 0

摘要

我们考虑在势函数r以亚线性速度增加到无穷大，粒子密度有界的情况下的平均场零范围过程。确定了系统的混合时间，并建立了截止时间。我们还证明了庞加莱常数在零和无穷之间有界。这种平均场估计通过比较参数扩展到任意几何形状。我们的证明使用了Bubley和Dyer的路径耦合方法和随机微积分。

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The mean-field zero-range process with unbounded monotone rates: Mixing time, cutoff, and Poincaré constant

We consider the mean-field Zero-Range process in the regime where the potential function $r$ is increasing to infinity at sublinear speed, and the density of particles is bounded. We determine the mixing time of the system, and establish cutoff. We also prove that the Poincare constant is bounded away from zero and infinity. This mean-field estimate extends to arbitrary geometries via a comparison argument. Our proof uses the path-coupling method of Bubley and Dyer and stochastic calculus.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.