On a random entanglement problem

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...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 87; no. 6; pp. 1090 - 1120
Main Authors Bonner, Gage, Thiffeault, Jean-Luc, Valkó, Benedek
Format Journal Article
LanguageEnglish
Published 30.12.2022
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Summary: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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxac031