Counting limit theorems for representations of Gromov-hyperbolic groups

08.11.2022 10:30

Let G be a Gromov-hyperbolic group and F a finite symmetricgenerating set. The choice of S determines a metric on G (namely the graph metric on the associated Cayley graph). Given a representation of G in 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 G 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. If time allows, we will also see boundary limit theorems and convergence of interpolated matrix norms along geodesic rays to the standard Brownian motion. The connections with the results of Lubotzky--Mozes--Raghunathan and Kaimanovich--Kapovich--Schupp will also be
discussed. Joint work with Stephen Cantrell.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05,Tuesday 8.11.2022, Séminaire Groupes et géométrie

entrée libre