Constructive approach to limit theorems for recurrent diffusive random walks on a strip

Author:

Dolgopyat Dmitry1,Goldsheid Ilya2

Affiliation:

1. Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA

2. School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, Great Britain

Abstract

We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of environment viewed by the particle process. Our conditions can be verified for a wide class of environments including independent environments, quasiperiodic environments, and environments which are asymptotically constant at infinity. The conditions presented deal with a fixed environment, in particular, no stationarity conditions are imposed.

Publisher

IOS Press

Subject

General Mathematics

Reference49 articles.

1. Asymptotic behaviour for random walks in random environments;Alili;J. Appl. Prob.,1999

2. Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments;Berger;Ann. Probab.,2016

3. G. Birkhoff, Lattice Theory, 3rd edn, AMS Colloquium Publications, Vol. 25, Prvidence, Rhode Island, 1973, vi+418 pp.

4. Exact convergence rates in some martingale central limit theorems;Bolthausen;Ann. Probab.,1982

5. Recurrence and transience of random walks in random environments on a strip;Bolthausen;Comm. Math. Phys.,2000

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3