Counting limit theorems for representations of Gromov-hyperbolic groups

Cagri Sert (U Zürich)

Jul 21. 2023, 14:00 — 14:40

Let G be a Gromov-hyperbolic group and S a finite symmetric generating 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 establishing statistical results analogous to random matrix products theory (RMPT) but for the deterministic sequence of spherical averages (with respect to S-metric). 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 (and results in) the classical RMPT, a result of Lubotzky--Mozes--Raghunathan and a question of Kaimanovich--Kapovich--Schupp will be discussed. Joint work with S. Cantrell.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics (Workshop)
Christopher Cashen (U of Vienna)
Javier de la Nuez González (KIAS, Seoul)
Alexandra Edletzberger (U of Vienna)
Yash Lodha (U of Hawaii, Honolulu)