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arXiv · 2506.04124

H\"older continuity of Lyapunov exponents for non-invertible and non-compact random cocycles

Pedro Duarte·Tomé Graxinha
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Abstract

We study the regularity of Lyapunov exponents for random linear cocycles taking values in $\Mat_m(\R)$ and driven by i.i.d. processes. Under three natural conditions - finite exponential moments, a spectral gap between the top two Lyapunov exponents, and quasi-irreducibility of the associated semigroup - we prove that the top Lyapunov exponent is H\"older continuous with respect to the Wasserstein distance. In the final section, we apply the main results to Schr\"odinger cocycles with unbounded potentials.

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Pedro Duarte, Tomé Graxinha. 2025-06-04. H\"older continuity of Lyapunov exponents for non-invertible and non-compact random cocycles. https://arxiv.org/abs/2506.04124

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