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  1. Home > Articles & Issues >
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  3. A Markov Chain Algor ...
Conference paper

A Markov Chain Algorithm for determining Crossing Times through nested Graphs

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]
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Proceedings
DOI
10.46298/dmtcs.3587
License
https://about.hal.science/hal-authorisation-v1
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A Markov Chain Algorithm for determining Crossing Times through nested Graphs

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]
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 $K$.
Keywords
  • [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]
  • (nested) fractal
  • self―similarity
  • walk dimension
  • crossing time
Cited by

Source: OpenCitations

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    Discrete and Continuous Dynamical Systems - B

    Authors : Uta Renata Freiberg ORCID

    Journal reference : Volume 17, 2011, pp. 509-525

    DOI : 10.3934/dcdsb.2012.17.509

  • Exact Computation and Approximation of Stochastic and Analytic Parameters of Generalized Sierpinski Gaskets

    Methodology And Computing In Applied Probability

    Authors : Uta Freiberg ORCID, Christoph Thäle

    Journal reference : Volume 15, 2011, pp. 485-509

    DOI : 10.1007/s11009-011-9254-7

  • Some Remarks on the Hausdorff and Spectral Dimension of V-Variable Nested Fractals

    Applied and numerical harmonic analysis

    Authors : Uta Renata Freiberg ORCID

    Journal reference : Volume , 2010, pp. 267-282

    DOI : 10.1007/978-0-8176-4888-6_17
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