Dirichlet forms on fractals: Poincaré constant and resistance

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Abstract

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. © 1992 Springer-Verlag.

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APA

Kusuoka, S., & Yin, Z. X. (1992). Dirichlet forms on fractals: Poincaré constant and resistance. Probability Theory and Related Fields, 93(2), 169–196. https://doi.org/10.1007/BF01195228

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