Methodology and Computing in Applied Probability

, Volume 15, Issue 3, pp 485–509

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

Article

Abstract

The interplay of fractal geometry, analysis and stochastics on the one-parameter 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.

Keywords

Crossing time Einstein relation Fractal geometry Hausdorff dimension Rotor walks Sierpinski gasket Spectral dimension Walk dimension 

AMS 2000 Subject Classifications

28A80 60J10 65C50 05C81 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of SiegenSiegenGermany
  2. 2.Department of MathematicsUniversity of FribourgFribourgSwitzerland
  3. 3.Institute of MathematicsUniversity of OsnabrückOsnabrückGermany

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