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

Uta Freiberg () and Christoph Thäle ()
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Uta Freiberg: University of Siegen
Christoph Thäle: University of Fribourg

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 3, 485-509

Abstract: 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; 28A80; 60J10; 65C50; 05C81 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9254-7

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