Random walks on hyperbolic groups and their Riemann surfaces

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dc.creatorNechaev, Sergei
dc.creatorVoituriez, Raphael
dc.date2000-12-20
dc.date.accessioned2026-07-07T04:28:13Z
dc.date.available2026-07-07T04:28:13Z
dc.descriptionWe 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.
dc.description29 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0012037
dc.identifierhttp://arxiv.org/abs/math-ph/0012037
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56704
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.titleRandom walks on hyperbolic groups and their Riemann surfaces
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