On the distribution of the periods of convex representations I

TL;DR

This paper establishes a central limit theorem for certain cocycles associated with convex representations of hyperbolic groups, providing new probabilistic insights into their distributional properties.

Contribution

It introduces a central limit theorem for H"older continuous cocycles in the context of convex and irreducible rational representations of hyperbolic groups.

Findings

Proves a central limit theorem for specific cocycles.

Applies results to convex representations of hyperbolic groups.

Enhances understanding of distributional behavior in geometric group theory.

Abstract

We prove a central limit theorem for a class of H\"older continuous cocycles with an application to stricly convex and irreducible rational representations of hyperbolic groups, introduced by Sambarino [Quantitative properties of convexe representations. Comment. Math. Helv 89 (2014), 443-488].