Abstract
We define a new Markov chain on the symbolic space representing the Sierpinski gasket (SG), and show that the corresponding Martin boundary is homeomorphic to the SG while the minimal Martin boundary is the three vertices of the SG. In addition, the harmonic structure induced by the Markov chain coincides with the canonical one on the SG. This suggests another approach to consider the existence of Laplacians on those self-similar sets for which the problem is still not settled.
| Original language | English |
|---|---|
| Pages (from-to) | 475-494 |
| Number of pages | 20 |
| Journal | Science China Mathematics |
| Volume | 55 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 2012 |
Scopus Subject Areas
- General Mathematics
Keywords
- Green function
- Markov chain
- Martin boundary
- Sierpinski gasket
- fractal
- harmonic function
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