Easy estimates of Lyapunov exponents for random products of matrices
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915972699389952 |
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| author | Nabahi, Nadya Shpilrain, Vladimir |
| author_facet | Nabahi, Nadya Shpilrain, Vladimir |
| contents | The problems that we consider in this paper are as follows. Let $A_1, \ldots, A_k$ be square matrices (over reals). Let $W=w(A_1, \ldots, A_k)$ be a random product of $n$ matrices. What is the expected absolute value of the largest (in the absolute value) entry in such a random product? What is the (maximal) Lyapunov exponent for a random matrix product like that? We give an answer to the first question under some mild restrictions on the entries of $A_i$. For the second question, we offer a very simple and efficient method to produce an upper bound on the Lyapunov exponent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_18944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Easy estimates of Lyapunov exponents for random products of matrices Nabahi, Nadya Shpilrain, Vladimir Group Theory Dynamical Systems The problems that we consider in this paper are as follows. Let $A_1, \ldots, A_k$ be square matrices (over reals). Let $W=w(A_1, \ldots, A_k)$ be a random product of $n$ matrices. What is the expected absolute value of the largest (in the absolute value) entry in such a random product? What is the (maximal) Lyapunov exponent for a random matrix product like that? We give an answer to the first question under some mild restrictions on the entries of $A_i$. For the second question, we offer a very simple and efficient method to produce an upper bound on the Lyapunov exponent. |
| title | Easy estimates of Lyapunov exponents for random products of matrices |
| topic | Group Theory Dynamical Systems |
| url | https://arxiv.org/abs/2509.18944 |