3 citations · 6 across the 5 of their papers we have counts for
6 papers
Busemann points are nowhere dense
Aitor Azemar, Maxime Fortier Bourque
We prove that the set of Busemann points (the limits of almost-geodesic rays) is nowhere dense in the horoboundary of the Teichmüller metric for all Teichmüller spaces of complex d…
Stationary measures on the circle from hyperbolic surfaces with cusps cannot be straightened by quasi-symmetries
Aitor Azemar, Vaibhav Gadre
Stationary measures on the circle that arise from a large class of random walks on the fundamental group of a finite-area complete hyperbolic surface with cusps are singular with r…
Bounds for the random walk speed in terms of the Teichmüller distance
Aitor Azemar
Consider a closed surface with negative Euler characteristic, and an admissible probability measure on the fundamental group of with finite first moment with respect to som…
Random walk speed is a proper function on Teichmüller space
Aitor Azemar, Vaibhav Gadre, Sébastien Gouëzel +3
Consider a closed surface with negative Euler characteristic, and an admissible probability measure on the fundamental group of with finite first moment. Corresponding to e…
A qualitative description of the horoboundary of the Teichmüller metric
Aitor Azemar
Two commonly studied compactifications of Teichmüller spaces of finite type surfaces with respect to the Teichmüller metric are the horofunction and visual compactifications. We sh…
Random walks on Convergence Groups
Aitor Azemar
We extend some properties of random walks on hyperbolic groups to random walks on convergence groups. In particular we prove that if a convergence group acts on a compact metri…