On a random entanglement problem
Abstract
We study a model for the entanglement of a twodimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.08524
 arXiv:
 arXiv:2010.08524
 Bibcode:
 2020arXiv201008524B
 Keywords:

 Mathematics  Probability
 EPrint:
 30 pages, 5 figures. AMSart style with Tikz