Exact computation and approximation of stochastic and analytic parameters of generalized Sierpinski gaskets
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Freiberg, Uta
University of Siegen, Emmy-Noether-Campus, Siegen, Germany
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Thäle, Christoph
Department of Mathematics, University of Fribourg, Switzerland - Institute of Mathematics, University of Osnabrück, Germany
Published in:
- Methodology and Computing in Applied Probability. - 2011, vol. 15, no. 3, p. 485-509
English
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.
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Faculty
- Faculté des sciences et de médecine
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Department
- Département de Mathématiques
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Language
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Classification
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Mathematics
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License
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License undefined
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Identifiers
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Persistent URL
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https://folia.unifr.ch/unifr/documents/302126
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