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RANDOM WALKS, SELF-AVOIDING WALKS AND 1/f NOISE ON FINITE LATTICES

FERDINAND GRÜNEIS

Institut für Angewandte Stochastik, Friedrich-Herschelstr. 4, 81679 München, Germany

https://doi.org/10.1142/S0219477504002117Cited by:1 (Source: Crossref)

Abstract

We investigate the probabilities for a return to the origin at step n of a random walker on a finite lattice. As a consistent measure only the first returns to the origin appear to be of relevance; these include paths with self-intersections and self-avoiding polygons. Their return probabilities are power-law distributed giving rise to 1/f^b noise. Most striking is the behavior of the self-avoiding polygons exhibiting a slope b=0.83 for d=2 and b=0.93 for d=3 independent on lattice structure.

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