Asymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment

Journal article

Asymptotically one-dimensional diffusions on the Sierpinski gasket constitute a one parameter family of processes with significantly different behaviour to the Brownian motion. Due to homogenization effects they behave globally like the Brownian motion, yet locally they have a preferred direction of motion. We calculate the spectral dimension for these processes and obtain short time heat kernel estimates in the Euclidean metric. The results are derived using branching process techniques, and...

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Authors: Hambly, B; Jones, O

• Publication status: Published
• Journal: JOURNAL OF THEORETICAL PROBABILITY
• Volume: 15
• Issue: 2
• Pages: 285-322
• Publication date: 2002-04-01
• DOI: 10.1023/A:1014858709284
• ISSN: 0894-9840
• Language: English
• Keywords: diffusion; varying environment; spectral dimension; branching process; Sierpinski gasket; fractal; multi-type; heat kernel