On a random entanglement problem
Probability
2020-10-19 v1
Abstract
We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental groupoid of the region. We quantify entanglement of the path with the length of the appropriate element in this groupoid. Our main results are a law of large numbers and a central limit theorem for this quantity. The constants appearing in the limit theorems are expressed in terms of a coupled system of quadratic equations.
Cite
@article{arxiv.2010.08524,
title = {On a random entanglement problem},
author = {Gage Bonner and Jean-Luc Thiffeault and Benedek Valko},
journal= {arXiv preprint arXiv:2010.08524},
year = {2020}
}
Comments
30 pages, 5 figures. AMSart style with Tikz