Simple Random Walks on Tori
Abstract
We consider a Markov chain whose phase space is a ddimensional 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.
 Publication:

Journal of Statistical Physics
 Pub Date:
 February 1999
 DOI:
 10.1023/A:1004564824697
 Bibcode:
 1999JSP....94..695S
 Keywords:

 Markov chain;
 homological equation;
 Levy excursion;
 stable law