Continuity of the Lyapunov exponents of non-invertible random cocycles with constant rank

TL;DR

This paper proves that Lyapunov exponents for certain non-invertible random cocycles with constant rank vary continuously and satisfy large deviations estimates, enhancing understanding of their stability.

Contribution

It establishes the uniform large deviations estimates and H"older continuity of Lyapunov exponents for non-invertible cocycles with constant rank, a novel result in this context.

Findings

Lyapunov exponents are H"older continuous

Large deviations estimates are established

Results apply to non-invertible cocycles with constant rank

Abstract

In this paper we establish uniform large deviations estimates of exponential type and H\"older continuity of the Lyapunov exponents for random non-invertible cocycles with constant rank.