A Markov Chain Algorithm for determining Crossing Times through nested Graphs

Abstract : According to the by now established theory developed in order to define a Laplacian or ― equivalently ― a Brownian motion on a nested fractal, one has to solve certain renormalization problems. In this paper, we present a Markov chain algorithm solving the problem for certain classes of simple fractals $K$ provided that there exists a unique Brownian motion and hence, a unique Laplacian on $K$.
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Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.501-518, 2008, DMTCS Proceedings
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Uta Freiberg, Christoph Thäle. A Markov Chain Algorithm for determining Crossing Times through nested Graphs. Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.501-518, 2008, DMTCS Proceedings. 〈hal-01194670〉

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