ISSN:
1572-9613
Keywords:
Random walk statistics
;
fractal structures
;
spectral dimension
;
percolation clusters
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01012921
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