Dominated Representations, Intersections and Large Deviations

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large deviation principle
hyperbolic group
Patterson-Sullivan measure

Appears in collection : French Japanese Conference on Probability and Interactions

We show that mean distortions and growth rates determine rough similarity classes of hyperbolic metrics in groups, and discuss its relation to the rigidity of dominated representations and concentration phenomena for counting measures on large balls. Joint work with Stephen Cantrell (Warwick).