Winding angle distribution of 2D random walks with traps

摘要

We study analytically the asymptotic behaviour of he 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) similar to exp(-c root t)(1+x(2))(-1) with x similar to n/root t, where the first exponent represents a well known longtime tail of the probability that a particle will not be trapped. [References: 16]