Central limit theorems for counting measures in coarse negative curvature

Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo

Research output: Contribution to journalArticlepeer-review

Abstract

We establish central limit theorems for an action of a group on a hyperbolic space with respect to the counting measure on a Cayley graph of. 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.

Original languageEnglish
Pages (from-to)1980-2013
Number of pages34
JournalCompositio Mathematica
Volume158
Issue number10
DOIs
StatePublished - 3 Oct 2022

Keywords

  • central limit theorem
  • counting measure
  • displacement
  • group actions
  • hyperbolic spaces
  • random walk
  • translation length

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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