Winding angle distribution of 2D random walks with traps
Statistical Mechanics
2009-10-31 v1 Disordered Systems and Neural Networks
Abstract
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.
Cite
@article{arxiv.cond-mat/9809389,
title = {Winding angle distribution of 2D random walks with traps},
author = {K. Samokhin},
journal= {arXiv preprint arXiv:cond-mat/9809389},
year = {2009}
}
Comments
RevTeX, 6 pages, 1 postscript figure, to be published in J. Phys. A