Extremal random matrices with independent entries and matrix superconcentration inequalities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909543716356096 |
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| author | Brailovskaya, Tatiana van Handel, Ramon |
| author_facet | Brailovskaya, Tatiana van Handel, Ramon |
| contents | We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds in this setting due to Bandeira and Van Handel, and establishes the best possible tail behavior for random matrices with an arbitrary variance pattern. These bounds arise from an extremum problem for nonhomogeneous random matrices: among all variance patterns with a given sparsity parameter, the moments of the random matrix are maximized by block-diagonal matrices with i.i.d. entries in each block. As part of the proof, we obtain sharp bounds on large moments of Gaussian Wishart matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extremal random matrices with independent entries and matrix superconcentration inequalities Brailovskaya, Tatiana van Handel, Ramon Probability 60B20, 60E15, 46L53, 46L54, 15B52 We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds in this setting due to Bandeira and Van Handel, and establishes the best possible tail behavior for random matrices with an arbitrary variance pattern. These bounds arise from an extremum problem for nonhomogeneous random matrices: among all variance patterns with a given sparsity parameter, the moments of the random matrix are maximized by block-diagonal matrices with i.i.d. entries in each block. As part of the proof, we obtain sharp bounds on large moments of Gaussian Wishart matrices. |
| title | Extremal random matrices with independent entries and matrix superconcentration inequalities |
| topic | Probability 60B20, 60E15, 46L53, 46L54, 15B52 |
| url | https://arxiv.org/abs/2401.06284 |