Sierpinski gasket as a Martin boundary I: Martin kernels - Dedicated to Professor Masatoshi Fukushima on the occasion of his 60th birthday

Abstract

We show that a Sierpinski gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.