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Random walks on the braid group B_3 and magnetic translations in hyperbolic geometry

R. Voituriez
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Abstract

We study random walks on the three-strand braid group $B_3$, and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of $B_3$ as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane.

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R. Voituriez. 2001-11-19. Random walks on the braid group B_3 and magnetic translations in hyperbolic geometry. https://doi.org/10.1016/s0550-3213(01)00590-9

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