Hölder continuity of Lyapunov exponents for non-invertible and non-compact random cocycles
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908393528098816 |
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| author | Duarte, Pedro Graxinha, Tomé |
| author_facet | Duarte, Pedro Graxinha, Tomé |
| contents | 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 Hölder continuous with respect to the Wasserstein distance. In the final section, we apply the main results to Schrödinger cocycles with unbounded potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder continuity of Lyapunov exponents for non-invertible and non-compact random cocycles Duarte, Pedro Graxinha, Tomé Dynamical Systems 37H15, 37A30 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 Hölder continuous with respect to the Wasserstein distance. In the final section, we apply the main results to Schrödinger cocycles with unbounded potentials. |
| title | Hölder continuity of Lyapunov exponents for non-invertible and non-compact random cocycles |
| topic | Dynamical Systems 37H15, 37A30 |
| url | https://arxiv.org/abs/2506.04124 |