Randomly growing braid on three strands and the manta ray

Jean Mairesse, Frédéric Mathéus

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 wal…