The asymptotic properties of cusp excursions in hyperbolic manifolds are famously quantified by Sullivan's logarithm law, which relates the depth of excursion with the Hausdorff dimension of the limit set. In this talk, we extend this work to Hilbert geometries, proving a global shadow lemma and a logarithm law for Patterson-Sullivan measures in geometrically finite Hilbert manifolds.
We also prove a Dirichlet-type theorem for hyperbolic metric spaces which have sufficiently regular Busemann functions. Joint work with Harry Bray.

https://umich.zoom.us/j/97288641488 Speaker(s): Giulio Tiozzo (University of Toronto)