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Counting problems in graph products and relatively hyperbolic groups (1711.04177v1)
Published 11 Nov 2017 in math.GT, math.DS, and math.GR
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) and translation length grows linearly. We provide applications to a large class of relatively hyperbolic groups and graph products, including right-angled Artin groups and right-angled Coxeter groups.
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