Dirichlet forms on fractals: Poincaré constant and resistance
- 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.