Exact Computation and Approximation of Stochastic and Analytic Parameters of Generalized Sierpinski Gaskets
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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.
KeywordsCrossing time Einstein relation Fractal geometry Hausdorff dimension Rotor walks Sierpinski gasket Spectral dimension Walk dimension
AMS 2000 Subject Classifications28A80 60J10 65C50 05C81
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