The Sierpiński gasket as the Martin boundary of a nonisotropic Markov chain
Abstract
In 2012 Lau and Ngai, motivated by the work of Denker and Sato, gave an example of an isotropic Markov chain on the set of finite words over a three letter alphabet, whose Martin boundary is homeomorphic to the Sierpiński gasket. Here, we extend the results of Lau and Ngai to a class of nonisotropic Markov chains. We determine the Martin boundary and show that the minimal Martin boundary is a proper subset of the Martin boundary. In addition, we give a description of the set of harmonic functions.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.04414
 Bibcode:
 2017arXiv171004414K
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Probability;
 31C35;
 60J50;
 28A80;
 60J10
 EPrint:
 13 pages, 5 figures