Operator $\ell^\infty \to \ell^\infty$ norm of products of random matrices
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915734885498880 |
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| author | Mourrat, Jean-Christophe |
| author_facet | Mourrat, Jean-Christophe |
| contents | We study the $\ell^\infty \to \ell^\infty$ operator norm of products of independent random matrices with independent and identically distributed entries. For $n$-by-$n$ matrices whose entries are centered, have unit variance, and have a finite moment of order $4α$ for some $α> 1$, we find that the operator norm of the product of $p$ matrices behaves asymptotically like $n^{\frac {p+1}{2}}\sqrt{2/π}$. The case of products of possibly non-square matrices with possibly non-centered entries is also covered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator $\ell^\infty \to \ell^\infty$ norm of products of random matrices Mourrat, Jean-Christophe Probability 60B20 We study the $\ell^\infty \to \ell^\infty$ operator norm of products of independent random matrices with independent and identically distributed entries. For $n$-by-$n$ matrices whose entries are centered, have unit variance, and have a finite moment of order $4α$ for some $α> 1$, we find that the operator norm of the product of $p$ matrices behaves asymptotically like $n^{\frac {p+1}{2}}\sqrt{2/π}$. The case of products of possibly non-square matrices with possibly non-centered entries is also covered. |
| title | Operator $\ell^\infty \to \ell^\infty$ norm of products of random matrices |
| topic | Probability 60B20 |
| url | https://arxiv.org/abs/2502.06711 |