On a random entanglement problem

Gage Bonner; Jean-Luc Thiffeault; Benedek Valko

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arXiv · 2010.08524

On a random entanglement problem

Gage Bonner·Jean-Luc Thiffeault·Benedek Valko

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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.

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Gage Bonner, Jean-Luc Thiffeault, Benedek Valko. 2020-10-16. On a random entanglement problem. https://arxiv.org/abs/2010.08524

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