Faculté des sciences

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

Freiberg, Uta ; Thäle, Christoph

In: Methodology and Computing in Applied Probability, 2011, p. -

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... Plus

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    Summary
    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.