Simple random walks on tori

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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 languageEnglish (US)
Pages (from-to)695-708
Number of pages14
JournalJournal of Statistical Physics
Volume94
Issue number3-4
DOIs
StatePublished - 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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