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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Rammal, R. Random walk statistics on fractal structures. J Stat Phys 36, 547–560 (1984). https://doi.org/10.1007/BF01012921
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DOI: https://doi.org/10.1007/BF01012921