Asymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment
Asymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment
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 we give estimates for the left tail of the limiting distribution for a supercritical multi-type branching process with varying environment.
diffusion, fractal, sierpinski gasket, spectral dimension, heat kernel, branching process, multi-type, varying environment
285-322
Hambly, B.M.
953396cd-aad7-4dee-8a16-af59a067eff2
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
2002
Hambly, B.M.
953396cd-aad7-4dee-8a16-af59a067eff2
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
Hambly, B.M. and Jones, O.D.
(2002)
Asymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment.
Journal of Theoretical Probability, 15 (2), .
(doi:10.1023/A:1014858709284).
Abstract
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 we give estimates for the left tail of the limiting distribution for a supercritical multi-type branching process with varying environment.
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Published date: 2002
Keywords:
diffusion, fractal, sierpinski gasket, spectral dimension, heat kernel, branching process, multi-type, varying environment
Organisations:
Operational Research
Identifiers
Local EPrints ID: 29686
URI: http://eprints.soton.ac.uk/id/eprint/29686
ISSN: 0894-9840
PURE UUID: c344e937-ca85-48c6-97c2-8da3bac35984
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Date deposited: 12 May 2006
Last modified: 15 Mar 2024 07:33
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Author:
B.M. Hambly
Author:
O.D. Jones
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