Random walks on hyperbolic groups and their Riemann surfaces
Abstract
We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the drift in different cases, including the braid group $B_3$. We also compute in this case the return probability. The action of these groups on the hyperbolic plane is investigated, and the distribution of a geometric invariant, the hyperbolic distance, is given. These two invariants are shown to be related by a closed formula.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2000
- DOI:
- 10.48550/arXiv.math-ph/0012037
- arXiv:
- arXiv:math-ph/0012037
- Bibcode:
- 2000math.ph..12037N
- Keywords:
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- Mathematical Physics;
- Statistical Mechanics
- E-Print:
- 29 pages, 8 figures