Central limit theorem for linear groups

TL;DR

This paper establishes a central limit theorem for random walks with finite variance on linear groups, providing a probabilistic understanding of their asymptotic behavior.

Contribution

It introduces a new CLT result specifically for random walks on linear groups, extending classical probability theory to this algebraic setting.

Findings

Proves a CLT for finite variance random walks on linear groups

Describes the asymptotic distribution of such random walks

Extends probabilistic methods to algebraic group contexts

Abstract

We prove a central limit theorem for random walks with finite variance on linear groups.