Transition probabilities for the simple random walk on the Sierpinski graph (Q1915824)
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scientific article; zbMATH DE number 894787
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transition probabilities for the simple random walk on the Sierpinski graph |
scientific article; zbMATH DE number 894787 |
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Transition probabilities for the simple random walk on the Sierpinski graph (English)
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5 August 1996
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Similar to the upper and lower bounds for the density of Brownian motion on the Sierpinski gasket [see \textit{M. T. Barlow} and \textit{E. A. Perkins}, Probab. Theory Relat. Fields 79, No. 4, 543-623 (1988; Zbl 0635.60090)], the transition probability \(p_t (x, y)\) of a simple random walk on the Sierpinski graph, a pre-fractal subgraph of the Sierpinski gasket, is obtained, as \(t>|x-y |\). A comparison of this result to that for a random walk on a general graph is shown.
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random walk
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fractal
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transition probability
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Brownian motion on the Sierpinski gasket
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