Central Limit Theorem for non-stationary random products of $\SL(2, \R)$ matrices

TL;DR

This paper establishes a Central Limit Theorem for non-stationary sequences of random matrices in SL(2, R), extending classical iid results to more general, non-stationary contexts.

Contribution

It generalizes the classical CLT for iid matrix products to non-stationary sequences in SL(2, R), broadening the scope of probabilistic limit theorems in matrix products.

Findings

Proves CLT for non-stationary SL(2, R) matrix products

Extends classical iid results to non-stationary cases

Provides new tools for analyzing non-stationary matrix sequences

Abstract

We prove Central Limit Theorem for non-stationary random products of $SL(2, \mathbb{R})$ matrices, generalizing the classical results by Le Page and Tutubalin that were obtained in the case of iid random matrix products.