On the distribution of the periods of convex representations II

TL;DR

This paper proves a central limit theorem for the distribution of periods in convex representations of hyperbolic groups, advancing understanding of their statistical properties.

Contribution

It establishes a central limit theorem for the periods of Zariski dense convex representations of hyperbolic groups, a novel result in the field.

Findings

Central limit theorem for periods of convex representations

Statistical distribution characterized for Zariski dense representations

Enhanced understanding of geometric group representations

Abstract

Let $\rho : \Gamma \longrightarrow G$ be a Zariski dense irreducible convex representation of the hyperbolic group $\Gamma$, where G is a connected real semisimple algebraic Lie group. We establish a central limit type theorem for the periods of the representation $\rho$.