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.
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Kusuoka, S., Yin, Z.X. Dirichlet forms on fractals: Poincaré constant and resistance. Probab. Th. Rel. Fields 93, 169–196 (1992). https://doi.org/10.1007/BF01195228
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DOI: https://doi.org/10.1007/BF01195228