Simple random walks on tori

Ya G. Sinai

doi:10.1023/a:1004564824697

Simple random walks on tori

Ya G. Sinai

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We consider a Markov chain whose phase space is a d-dimensional torus. A point x jumps to x + ω with probability p(x) and to x - ω with probability 1 - p(x). For Diophantine ω and smooth p we prove that this Markov chain has an absolutely continuous invariant measure and the distribution of any point after n steps converges to this measure.

Original language	English (US)
Pages (from-to)	695-708
Number of pages	14
Journal	Journal of Statistical Physics
Volume	94
Issue number	3-4
DOIs	https://doi.org/10.1023/a:1004564824697
State	Published - Feb 1999

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Homological equation
Levy excursion
Markov chain
Stable law

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10.1023/a:1004564824697

Cite this

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title = "Simple random walks on tori",

abstract = "We consider a Markov chain whose phase space is a d-dimensional torus. A point x jumps to x + ω with probability p(x) and to x - ω with probability 1 - p(x). For Diophantine ω and smooth p we prove that this Markov chain has an absolutely continuous invariant measure and the distribution of any point after n steps converges to this measure.",

keywords = "Homological equation, Levy excursion, Markov chain, Stable law",

author = "Sinai, {Ya G.}",

year = "1999",

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T1 - Simple random walks on tori

AU - Sinai, Ya G.

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N2 - We consider a Markov chain whose phase space is a d-dimensional torus. A point x jumps to x + ω with probability p(x) and to x - ω with probability 1 - p(x). For Diophantine ω and smooth p we prove that this Markov chain has an absolutely continuous invariant measure and the distribution of any point after n steps converges to this measure.

AB - We consider a Markov chain whose phase space is a d-dimensional torus. A point x jumps to x + ω with probability p(x) and to x - ω with probability 1 - p(x). For Diophantine ω and smooth p we prove that this Markov chain has an absolutely continuous invariant measure and the distribution of any point after n steps converges to this measure.

KW - Homological equation

KW - Levy excursion

KW - Markov chain

KW - Stable law

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U2 - 10.1023/a:1004564824697

DO - 10.1023/a:1004564824697

M3 - Article

AN - SCOPUS:0039726821

SN - 0022-4715

VL - 94

SP - 695

EP - 708

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3-4

ER -

Simple random walks on tori

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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