Deviation Inequalities for the Spectral Norm of Structured Random Matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929340026978304 |
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| author | Dai, Guozheng Su, Zhonggen |
| author_facet | Dai, Guozheng Su, Zhonggen |
| contents | We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the $p$-th moment of the spectral norm by transfering the spectral norm into the suprema of canonical processes. A crucial ingredient of our proof is a comparison of weak and strong moments. As an application, we show a deviation inequality for the smallest singular value of a rectangular random matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deviation Inequalities for the Spectral Norm of Structured Random Matrices Dai, Guozheng Su, Zhonggen Probability We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the $p$-th moment of the spectral norm by transfering the spectral norm into the suprema of canonical processes. A crucial ingredient of our proof is a comparison of weak and strong moments. As an application, we show a deviation inequality for the smallest singular value of a rectangular random matrix. |
| title | Deviation Inequalities for the Spectral Norm of Structured Random Matrices |
| topic | Probability |
| url | https://arxiv.org/abs/2401.09263 |