Winding of geodesic rays chosen by a harmonic measure
Timoth\'ee B\'enard
TL;DR
This paper establishes limit theorems for the winding behavior of geodesic rays in hyperbolic spaces, with applications to harmonic measures and Patterson-Sullivan measures, advancing understanding of geometric and probabilistic properties.
Contribution
It introduces new limit theorems for homological winding of geodesic rays under harmonic measures in Gromov hyperbolic spaces, with applications to inverse problems and measure statistics.
Findings
Limit theorems for homological winding of geodesic rays.
Applications to inverse problems for harmonic measures.
Winding statistics for Patterson-Sullivan measures.
Abstract
We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain applications to the inverse problem for the harmonic measure, and winding statistics for Patterson-Sullivan measures.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Morphological variations and asymmetry · Point processes and geometric inequalities