Martin boundary and exit space on the Sierpinski gasketMartin boundary and exit space on the Sierpinski gasketMartin boundary and exit space on the Sierpinski gasket

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 coinci...

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Veröffentlicht in:中国科学:数学英文版 2012, Vol.55 (3), p.475-494
1. Verfasser: LAU Ka-Sing NGAI Sze-Man
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1674-7283
1869-1862