2022
DOI: 10.48550/arxiv.2201.00737
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Counting and boundary limit theorems for representations of Gromov-hyperbolic groups

Abstract: Given a Gromov-hyperbolic group G endowed with a finite symmetric generating set, we study the statistics of counting measures on the spheres of the associated Cayley graph under linear representations of G. More generally, we obtain a weak law of large numbers for subadditive functions, echoing the classical Fekete lemma. For strongly irreducible and proximal representations, we prove a counting central limit theorem with a Berry-Esseen type error rate and exponential large deviation estimates. Moreover, in t… Show more

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