Transition probabilities for the simple random walk on the Sierpinski graph
Transition probabilities for the simple random walk on the Sierpinski graph
Non-Gaussian upper and lower bounds are obtained for the transition probabilities of the simple random walk on the Sierpinski graph, the pre-fractal associated with the Sierpinski gasket. They are of the same form as bounds previously obtained for the transition density of Brownian motion on the Sierpinski gasket, subject to a scale restriction. A comparison with transition density bounds for random walks on general graphs demonstrates that this restriction represents the scale at which the pre-fractal graph starts to look like the fractal gasket.
heat transfer, chemical reaction, boundary layer, heat source, [ams classification codes] 60J15, random walk, fractal, transition probability
45-69
Motulevich, V.P.
c3ab2ffa-7427-4d0d-a308-3df4508d9700
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
1996
Motulevich, V.P.
c3ab2ffa-7427-4d0d-a308-3df4508d9700
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
Motulevich, V.P. and Jones, O.D.
(1996)
Transition probabilities for the simple random walk on the Sierpinski graph.
Stochastic Processes and their Applications, 61 (1), .
(doi:10.1016/0304-4149(95)00074-7).
Abstract
Non-Gaussian upper and lower bounds are obtained for the transition probabilities of the simple random walk on the Sierpinski graph, the pre-fractal associated with the Sierpinski gasket. They are of the same form as bounds previously obtained for the transition density of Brownian motion on the Sierpinski gasket, subject to a scale restriction. A comparison with transition density bounds for random walks on general graphs demonstrates that this restriction represents the scale at which the pre-fractal graph starts to look like the fractal gasket.
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Published date: 1996
Keywords:
heat transfer, chemical reaction, boundary layer, heat source, [ams classification codes] 60J15, random walk, fractal, transition probability
Organisations:
Operational Research
Identifiers
Local EPrints ID: 29678
URI: http://eprints.soton.ac.uk/id/eprint/29678
ISSN: 0304-4149
PURE UUID: f872e9fd-7294-4b98-bcd7-eb33177f67b1
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Date deposited: 14 Mar 2007
Last modified: 15 Mar 2024 07:33
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Author:
V.P. Motulevich
Author:
O.D. Jones
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