The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain

  title={The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain},
  author={Marc Kessebohmer and Tony Samuel and Karen L. Sender},
  journal={arXiv: Dynamical Systems},
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 Sierpinski gasket. Here, we extend the results of Lau and Ngai to a class of non-isotropic 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… 
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