Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909049373589504 |
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| author | Liu, Yingjian Viana, Marcelo |
| author_facet | Liu, Yingjian Viana, Marcelo |
| contents | 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-Hölder 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16718 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case Liu, Yingjian Viana, Marcelo Dynamical Systems Probability 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-Hölder 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. |
| title | Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2605.16718 |