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 language | English |
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Pages (from-to) | 1980-2013 |
Number of pages | 34 |
Journal | Compositio Mathematica |
Volume | 158 |
Issue number | 10 |
DOIs | |
State | Published - 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