Martin boundary and exit space on the Sierpinski gasket
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AbstractWe 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.
All Author(s) ListLau KS, Ngai SM
Journal nameScience China Mathematics
Year2012
Month3
Day1
Volume Number55
Issue Number3
PublisherSpringer Verlag (Germany)
Pages475 - 494
ISSN1674-7283
eISSN1869-1862
LanguagesEnglish-United Kingdom
Keywordsfractal; Green function; harmonic function; Markov chain; Martin boundary; Sierpinski gasket
Web of Science Subject CategoriesMathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2021-23-01 at 01:21