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Burau representation and random walk on string links

Xiao-Song Lin·Feng Tian·Zhenghan Wang
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Abstract

Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the transition matrix of a Markov process. For positive non-separable links, we show that all states are persistent. (This is an extensively revised version of the first author's original paper titled "Burau representation and random walk on knots".)

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BibTeXRIS

Xiao-Song Lin, Feng Tian, Zhenghan Wang. 1996-10-04. Burau representation and random walk on string links. https://arxiv.org/abs/q-alg/9605023

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