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

Autor(en): Freiberg, Uta
Thaele, Christoph
Stichwörter: Crossing time; Einstein relation; Fractal geometry; FRACTALS; Hausdorff dimension; Mathematics; Rotor walks; Sierpinski gasket; Spectral dimension; Statistics & Probability; Walk dimension
Erscheinungsdatum: 2013
Herausgeber: SPRINGER
Journal: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
Volumen: 15
Ausgabe: 3
Startseite: 485
Seitenende: 509
Zusammenfassung: 
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.
ISSN: 13875841
DOI: 10.1007/s11009-011-9254-7

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