We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e., they have full density with respect to counting in balls for the word metric in the Cayley graph) and translation length grows linearly. We provide applications to a large class of relatively hyperbolic groups and graph products, including all right-angled Artin groups and right-angled Coxeter groups.
Counting problems in graph products and relatively hyperbolic groups / Gekhtman, I.; Taylor, S. J.; Tiozzo, G.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 237:1(2020), pp. 311-371. [10.1007/s11856-020-2008-x]
Counting problems in graph products and relatively hyperbolic groups
Tiozzo G.
2020
Abstract
We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e., they have full density with respect to counting in balls for the word metric in the Cayley graph) and translation length grows linearly. We provide applications to a large class of relatively hyperbolic groups and graph products, including all right-angled Artin groups and right-angled Coxeter groups.| File | Dimensione | Formato | |
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