English

Central limit theorems for counting measures in coarse negative curvature

Dynamical Systems 2020-04-29 v1 Geometric Topology

Abstract

We establish central limit theorems for an action of a group G on a hyperbolic space X with respect to the counting measure on a Cayley graph of G. Our techniques allow us to remove the usual assumptions of properness and smoothness of the space, or cocompactness of the action. We provide several applications which require our general framework, including to lengths of geodesics in geometrically finite manifolds and to intersection numbers with submanifolds.

Keywords

Cite

@article{arxiv.2004.13084,
  title  = {Central limit theorems for counting measures in coarse negative curvature},
  author = {Ilya Gekhtman and Samuel J. Taylor and Giulio Tiozzo},
  journal= {arXiv preprint arXiv:2004.13084},
  year   = {2020}
}

Comments

36 pages

R2 v1 2026-06-23T15:08:04.470Z