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 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-04-21 DOI:10.1214/22-aap1851

Hong-Quan Tran

{"title":"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","authors":"Hong-Quan Tran","doi":"10.1214/22-aap1851","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The mean-field zero-range process with unbounded monotone rates: Mixing time, cutoff, and Poincaré constant\",\"authors\":\"Hong-Quan Tran\",\"doi\":\"10.1214/22-aap1851\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":50979,\"journal\":{\"name\":\"Annals of Applied Probability\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2021-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Applied Probability\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/22-aap1851\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-aap1851","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.