The Sierpinski gasket as Martin boundary: a non-isotropic case

Fractal Geometry and Dynamics

29 September 15:00 - 15:50

Karenina Sender - Universität Bremen

In the recent article "Martin boundary and exit space on the Sierpinski gasket", released 2012, Ka-Sing Lau and Sze-Man Ngai construct an isotropic Markov chain on the symbolic space which represents the Sierpinski gasket. They show that the Martin boundary of this chain is homeomorphic to the Sierpinski gasket, whereas the minimal Martin boundary is equal to the post critical set. Moreover, the induced harmonic functions on the Sierpinski gasket coincide with the canonical harmonic functions due to Kigami. In this talk we will see how these results can be generalised to a non-isotropic Markov chain.
Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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