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Randomly growing braid on three strands and the manta ray | | Jean Mairesse
; Frédéric Mathéus
; | | Date: |
30 Mar 2007 | | Journal: | Annals of Applied Probability 2007, Vol. 17, No. 2, 502-536 | | Subject: | Probability | | Abstract: | Consider the braid group $B_3=< a,b aba=bab>$ and the nearest neighbor random walk defined by a probability $
u$ 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. | | Source: | arXiv, math/0703913 | | Services: | Forum | Review | PDF | Favorites | |
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