Randomly growing braid on three strands and the manta ray

Details Randomly growing braid on three strands and the manta ray Randomly growing braid on three strands and the manta ray

2007-03-30

arxiv.org/abs/math/0703913v1

Annals of Applied Probability 2007, Vol. 17, No. 2, 502-536

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000754 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000754

Consider the braid group $B_3=< a,b| aba=bab>$ and the nearest neighbor random walk defined by a probability $\nu$ with support $\{a,a^{-1},b,b^{-1}\}$. The rate of escape of the walk is explicitly expressed in function of the unique solution of a set of eight polynomial equations of degree three over eight indeterminates. We also explicitly describe the harmonic measure of the induced random walk on $B_3$ quotiented by its center. The method and results apply, mutatis mutandis, to nearest neighbor random walks on dihedral Artin groups.

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