Transition probabilities for the simple random walk on the Sierpinski graph

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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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APA

Jones, O. D. (1996). Transition probabilities for the simple random walk on the Sierpinski graph. Stochastic Processes and Their Applications, 61(1), 45–69. https://doi.org/10.1016/0304-4149(95)00074-7

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