The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain
Research output: Contribution to journal › Article › peer-review
Authors
Colleges, School and Institutes
External organisations
- University of Bremen
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.
Details
| Original language | English |
|---|---|
| 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 |
| Publication status | E-pub ahead of print - 19 May 2020 |
Keywords
- Martin boundary, Markov chain, Green function, Harmonic function, Sierpinski gasket