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arXiv · 2605.16718

Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case

Yingjian Liu·Marcelo Viana
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Abstract

We study the regularity of Lyapunov exponents as functions on the space of compactly supported probability measures on $\mathrm{GL}(d,\mathbb{R})$. We prove that the Lyapunov exponents are pointwise log-H\"older continuous with respect to the Wasserstein distance, at semisimple probability measures with one-point Lyapunov spectrum. The proof relies on a decomposition of the action into virtually conformal subspaces and a Berry-Esseen type estimate for the random walk towards these subspaces.

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Yingjian Liu, Marcelo Viana. 2026-05-16. Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case. https://arxiv.org/abs/2605.16718

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