Spectral norm of matrices with independent entries up to polyloglog
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910004095746048 |
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| author | Meller, Rafał |
| author_facet | Meller, Rafał |
| contents | In this paper, we study the expectation of the operator norm of the random matrix (a_{ij} X_{ij}) for i,j <= n, under the assumption that the random variables (X_{ij}) are independent, symmetric and satisfy the moment growth condition ||X_{ij}||{2p} <= C ||X_{ij}||{p} for every p >= 1. We derive an upper bound expressed in terms of quantities that can be explicitly computed in many cases. This bound implies a two-sided estimate, up to a factor given by a power of an iterated logarithm. This factor is considerably smaller than the natural scale of the problem. Our result thus provides positive evidence supporting a conjecture formulated by Rafal Latala and Jan Swiatkowski. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral norm of matrices with independent entries up to polyloglog Meller, Rafał Probability Functional Analysis 60B20, 46B09 In this paper, we study the expectation of the operator norm of the random matrix (a_{ij} X_{ij}) for i,j <= n, under the assumption that the random variables (X_{ij}) are independent, symmetric and satisfy the moment growth condition ||X_{ij}||{2p} <= C ||X_{ij}||{p} for every p >= 1. We derive an upper bound expressed in terms of quantities that can be explicitly computed in many cases. This bound implies a two-sided estimate, up to a factor given by a power of an iterated logarithm. This factor is considerably smaller than the natural scale of the problem. Our result thus provides positive evidence supporting a conjecture formulated by Rafal Latala and Jan Swiatkowski. |
| title | Spectral norm of matrices with independent entries up to polyloglog |
| topic | Probability Functional Analysis 60B20, 46B09 |
| url | https://arxiv.org/abs/2512.23673 |