Analyticity of the Lyapunov exponents of random products of matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912837866094592 |
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| author | Amorim, Artur Durães, Marcelo Melo, Aline |
| author_facet | Amorim, Artur Durães, Marcelo Melo, Aline |
| contents | This paper is concerned with the study of random (Bernoulli and Markovian) product of matrices on a compact space of symbols. We establish the analyticity of the maximal Lyapunov exponent as a function of the transition probabilities, thus extending the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols. Our approach combines the spectral properties of the associated Markov operator with the theory of holomorphic functions in Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analyticity of the Lyapunov exponents of random products of matrices Amorim, Artur Durães, Marcelo Melo, Aline Dynamical Systems This paper is concerned with the study of random (Bernoulli and Markovian) product of matrices on a compact space of symbols. We establish the analyticity of the maximal Lyapunov exponent as a function of the transition probabilities, thus extending the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols. Our approach combines the spectral properties of the associated Markov operator with the theory of holomorphic functions in Banach spaces. |
| title | Analyticity of the Lyapunov exponents of random products of matrices |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.19286 |