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 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 functions.
Original language | English |
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Pages (from-to) | 113-136 |
Number of pages | 21 |
Journal | Journal of Fractal Geometry |
Volume | 7 |
Issue number | 2 |
Early online date | 19 May 2020 |
DOIs | |
Publication status | E-pub ahead of print - 19 May 2020 |
Keywords
- Green function
- Harmonic function
- Markov chain
- Martin boundary
- Sierpinski gasket