  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".)
