Large deviation principle for random matrix products

TL;DR

This paper extends Cramer's large deviation theorem from sums of independent real random variables to products of random matrices under a Zariski density assumption, broadening the scope of large deviation principles.

Contribution

It introduces a large deviation principle for random matrix products, generalizing classical results to a matrix setting under algebraic density conditions.

Findings

Established a large deviation principle for random matrix products.

Extended classical large deviation results to the matrix case.

Provided conditions under which the principle holds.

Abstract

Under a Zariski density assumption, we extend the classical theorem of Cramer on large deviations of sums of iid real random variables to random matrix products.