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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2505.07626 |
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| _version_ | 1866916733157113856 |
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| author | Mei, Jianzhang Liu, Quansheng |
| author_facet | Mei, Jianzhang Liu, Quansheng |
| contents | We consider the products $G_n = A_n \cdots A_1$ of independent and identical distributed nonnegative $d \times d$ matrices $(A_i)_{i \geq 1}$. For any starting point $x \in \mathbb{R}_+^d$ with unit norm, we establish the convergence to a stable law for the norm cocycle $\log | G_nx |$, jointly with its direction $G_n \cdot x = G_n x / | G_n x |$. We also prove a local limit theorem for the couple $ (\log |G_nx|, G_n \cdot x)$, and find the exact rate of its convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence to Stable Laws and a Local Limit Theorem for Products of Positive Random Matrices Mei, Jianzhang Liu, Quansheng Probability Primary: 60B10, 60G50, 60E07, Secondary: 60B20 We consider the products $G_n = A_n \cdots A_1$ of independent and identical distributed nonnegative $d \times d$ matrices $(A_i)_{i \geq 1}$. For any starting point $x \in \mathbb{R}_+^d$ with unit norm, we establish the convergence to a stable law for the norm cocycle $\log | G_nx |$, jointly with its direction $G_n \cdot x = G_n x / | G_n x |$. We also prove a local limit theorem for the couple $ (\log |G_nx|, G_n \cdot x)$, and find the exact rate of its convergence. |
| title | Convergence to Stable Laws and a Local Limit Theorem for Products of Positive Random Matrices |
| topic | Probability Primary: 60B10, 60G50, 60E07, Secondary: 60B20 |
| url | https://arxiv.org/abs/2505.07626 |