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.
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