704 citations · 2.4k across the 64 of their papers we have counts for
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Equidistribution of hyperbolic groups in homogeneous spaces
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We prove that infinite orbits of Zariski dense hyperbolic groups equidistribute in homogeneous spaces, in the sense that the family of measures obtained by averaging along spheres…
Metrics on trees I. The tower algorithm for interval maps
Giulio Tiozzo
We consider Milnor's "tower algorithm" in the space of piecewise monotone maps, an iterative algorithm on the space of metrics which unifies, on the one hand, Thurston's iterative…
Master Teapots and Entropy Algorithms for the Mandelbrot Set
Kathryn Lindsey, Giulio Tiozzo, Chenxi Wu
We construct an analogue of W. Thurston's "Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for…
A global shadow lemma and logarithm law for geometrically finite Hilbert geometries
Harrison Bray, Giulio Tiozzo
For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-…
The fundamental inequality for cocompact Fuchsian groups
Petr Kosenko, Giulio Tiozzo
We prove that the hitting measure is singular with respect to Lebesgue measure for any random walk on a cocompact Fuchsian group generated by translations joining opposite sides of…
Central limit theorems for counting measures in coarse negative curvature
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
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 remov…