# Winding angle distribution of 2D random walks with traps

Source: [Winding angle distribution of 2D random walks with traps](<https://www.sota2.com/research/paper/68fa24992c2a3760193a6596>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:20:15.324Z

Authors: K. Samokhin

Published: 1998-09-29T14:08:43.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9809389>)

[PDF](<https://arxiv.org/pdf/cond-mat/9809389.pdf>)