Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets
We consider homogeneous random Sierpinski carpets, a class of infinitely ramified random fractals which have spatial symmetry but which do not have exact self-similarity. For a fixed environment we construct"natural"diffusion processes on the fractal and obtain upper and lower estimates of the transition density for the process that are up to constants best possible. By considering the random case, when the environment is stationary and ergodic, we deduce estimates of Aronson type.
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 52(2), 373-408, 2000-04
The Mathematical Society of Japan