Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals

Presenters/Authors

• Sze-Man Ngai, Georgia Southern UniversityFollow
• Ka-Sing Lau, The Chinese University of Hong Kong

Document Type

Presentation

Presentation Date

9-10-2011

Copyright

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Abstract or Description

We define a Markov chain on a discrete symbolic space corresponding to the Sierpinski gasket (SG) and show that its Martin boundary is homeomorphic to the SG, while the minimal Martin boundary can be identified with the three vertices of the SG. Moreover, we show that the harmonic functions coincide with the standard ones. We also consider generalizations to a larger class of p.c.f. fractals. This is a joint work with Ka-Sing Lau.

Sponsorship/Conference/Institution

Northeastern Sectional Meeting of the American Mathematical Society (AMS)

Location

Ithaca, NY

Recommended Citation

Ngai, Sze-Man, Ka-Sing Lau. 2011. "Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals." Mathematical Sciences: Faculty Presentations (1991-2022). Presentation 347.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/347