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Dirichlet forms on fractals: Poincaré constant and resistance
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  • Published: June 1992

Dirichlet forms on fractals: Poincaré constant and resistance

  • Shigeo Kusuoka1 &
  • Zhou Xian Yin2 

Probability Theory and Related Fields volume 93, pages 169–196 (1992)Cite this article

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  • 91 Citations

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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.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Shigeo Kusuoka

  2. Department of Mathematics, Beijing Normal University, 100875, Beijing, People's Republic of China

    Zhou Xian Yin

Authors
  1. Shigeo Kusuoka
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  2. Zhou Xian Yin
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Partly supported by the JSPS Program

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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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  • Received: 17 September 1991

  • Revised: 03 February 1992

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01195228

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Mathematics Subject Classification

  • 60 J 60
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