Winding angle distribution of 2D random walks with traps

Details Winding angle distribution of 2D random walks with traps Winding angle distribution of 2D random walks with traps

1998-09-29

arxiv.org/abs/cond-mat/9809389v1

Physics

Condensed Matter

Statistical Mechanics

RevTeX, 6 pages, 1 postscript figure, to be published in J. Phys. A

Scientific paper

10.1088/0305-4470/31/44/007

We study analytically the asymptotic behaviour of the average probability P(n,t) for the trajectory of a 2D Brownian particle wandering in the presence of randomly distributed traps to wind n times around a given point after a time t. It is shown that P(n,t)\sim\exp(-c\sqrt{t}) (1+x^2)^{-1} with x\sim n/\sqrt{t}, where the first exponent represents a well known long-time tail of the probability that a particle will not be trapped.

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