Uta Freiberg ; Christoph Thäle - A Markov Chain Algorithm for determining Crossing Times through nested Graphs

dmtcs:3587 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science - https://doi.org/10.46298/dmtcs.3587
A Markov Chain Algorithm for determining Crossing Times through nested GraphsArticle

Authors: Uta Freiberg 1; Christoph Thäle 2,3

  • 1 Fakultät für Mathematik und Informatik [Jena]
  • 2 Département de Mathématiques - Université de Fribourg
  • 3 Département de Mathématiques [Fribourg]

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 $K$.


Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: (nested) fractal,self―similarity,walk dimension,crossing time,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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