, Volume 93, Issue 2, pp 169-196

Dirichlet forms on fractals: Poincaré constant and resistance

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Summary

We study Dirichlet forms associated with random walks on fractal-like finite grahs. We consider related Poincaré constants and resistance, and study their asymptotic behaviour. We construct a Markov semi-group on fractals as a subsequence of random walks, and study its properties. Finally we construct self-similar diffusion processes on fractals which have a certain recurrence property and plenty of symmetries.

Partly supported by the JSPS Program