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Journal article

Exact computation and approximation of stochastic and analytic parameters of generalized Sierpinski gaskets

  • Freiberg, Uta University of Siegen, Emmy-Noether-Campus, Siegen, Germany
  • Thäle, Christoph Department of Mathematics, University of Fribourg, Switzerland - Institute of Mathematics, University of Osnabrück, Germany
    04.10.2011
Published in:
  • Methodology and Computing in Applied Probability. - 2011, vol. 15, no. 3, p. 485-509
Crossing time
Einstein relation
Fractal geometry
Hausdorff dimension
Rotorwalks
Sierpinski gasket
Spectral dimension
Walk dimension
English The interplay of fractal geometry, analysis and stochastics on the oneparameter sequence of self-similar generalized Sierpinski gaskets is studied. An improved algorithm for the exact computation of mean crossing times through the generating graphs SG(m) of generalized Sierpinski gaskets sg(m) for m up to 37 is presented and numerical approximations up to m = 100 are shown. Moreover, an alternative method for the approximation of the mean crossing times, the walk and the spectral dimensions of these fractal sets based on quasi-random so-called rotor walks is developed, confidence bounds are calculated and numerical results are shown and compared with exact values (if available) and with known asymptotic formulas.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
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Persistent URL
https://folia.unifr.ch/unifr/documents/302126
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