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Article Dans Une Revue Israel Journal of Mathematics Année : 2017

On the genericity of loxodromic actions

Résumé

One way of picking a "generic" element of a finitely generated group is to pick a random element with uniform probability in a large ball centered on $1$ in the Cayley graph. If the group acts on a $\delta$-hyperbolic space, with at least one element acting loxodromically, then it is plausible that generic elements should act loxodromically with high probability. In this paper we prove that the probability of acting loxodromically is bounded away from 0, provided the group satisfies a very weak automaticity condition, and provided a certain compatibility condition linking the automatic with the $\delta$-hyperbolic structure is satisfied.

Dates et versions

hal-01016583 , version 1 (30-06-2014)

Identifiants

Citer

Bert Wiest. On the genericity of loxodromic actions. Israel Journal of Mathematics, 2017, 220 (2), pp.559-582. ⟨10.1007/s11856-017-1540-9⟩. ⟨hal-01016583⟩
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