Counting limit theorems for representations of Gromov-hyperbolic groups

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• Çağrı Sert (Universität Zürich)
• Wednesday 29 November 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

Let $\Gamma$ be a Gromov-hyperbolic group and $S$ a finite symmetric generating set. The choice of $S$ determines a metric on $\Gamma$ (namely the graph metric on the associated Cayley graph). Given a representation $\rho: \Gamma \to \GL_d(\R)$, we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to $S$-metric) for various numerical quantities (such as Euclidean norm) associated to elements of $\Gamma$ via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. The connections with the results of Lubotzky—Mozes—Raghunathan and Kaimanovich—Kapovich—Schupp will also be discussed. Joint work with Stephen Cantrell.

This talk is part of the Differential Geometry and Topology Seminar series.

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