Burau representation and random walks on string links

Xiao-Song Lin, Feng Tian and Zhenghan Wang

Vol. 182 (1998), No. 2, 289–302

DOI: 10.2140/pjm.1998.182.289

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.

Milestones

Received: 1 June 1996

Revised: 15 January 1997

Published: 1 February 1998