Randomly growing braid on three strands and the manta ray

Abstract

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.

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

References in corpus (2)

• Randomly growing braid on three strands and the manta ray
• Appendix to the paper "Randomly Growing Braid on Three Strands and the Manta Ray"

Cited by in corpus (11)

• Randomly growing braid on three strands and the manta ray
• Noncommutative independence from the braid group $B_{\infty }$
• Regularity of the entropy for random walks on hyperbolic groups
• Renewal theory for random walks on surface groups
• Differentiating the entropy of random walks on hyperbolic groups
• On the penetration distance in Garside monoids
• Regularity of the drift and entropy of random walks on groups
• Uniform measures on braid monoids and dual braid monoids
• Analyticity of the entropy for some random walks
• Rate of Escape on the Lamplighter Tree
• Rate of Escape on Free Products