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.
Categories: cond-mat.stat-mech cond-mat.dis-nn