Random walk statistics on fractal structures |
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Authors: | R Rammal |
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Institution: | (1) Centre de Recherches sur les Tres basses temperatures, C.N.R.S., B.P. 166X, 38042 Grenoble Cedex, France;(2) Department of Physics, University of Pennsylvania, 19104-3859 Philadelphia, Pennsylvania |
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Abstract: | We consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds: range, renewal theory, mean first passage time, etc. Asymptotic behaviors are shown to be controlled by the fractal (¯d) and spectral (¯d) dimensionalities of the considered structure. A simple decimation procedure giving the value of (¯d) is outlined and illustrated in the case of the Sierpinski gaskets. Recent results for the trapping problem, the self-avoiding walk, and the true-self-avoiding walk are briefly reviewed. New numerical results for diffusion on percolation clusters are also presented. |
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Keywords: | Random walk statistics fractal structures spectral dimension percolation clusters |
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