Probability Theory and Related Fields

, Volume 93, Issue 2, pp 169–196

Dirichlet forms on fractals: Poincaré constant and resistance

  • Shigeo Kusuoka
  • Zhou Xian Yin

DOI: 10.1007/BF01195228

Cite this article as:
Kusuoka, S. & Yin, Z.X. Probab. Th. Rel. Fields (1992) 93: 169. doi:10.1007/BF01195228


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.

Mathematics Subject Classification

60 J 60

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Shigeo Kusuoka
    • 1
  • Zhou Xian Yin
    • 2
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsBeijing Normal UniversityBeijingPeople's Republic of China