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math.GR2020★ 2 cited
An embedding of the Morse boundary in the Martin boundary
Matthew Cordes, Matthieu Dussaule, Ilya Gekhtman
We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities g…
math.DS2020
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…