On Log-Concave-Tailed Chaoses and the Restricted Isometry Property
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929340035366912 |
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| author | Dai, Guozheng Su, Zhonggen Ulyanov, Vladimir Wang, Hanchao |
| author_facet | Dai, Guozheng Su, Zhonggen Ulyanov, Vladimir Wang, Hanchao |
| contents | In this paper, we obtain a $p$-th moment bound for the suprema of a log-concave-tailed nonhomogeneous chaos process, which is optimal in some special cases. A crucial ingredient of the proof is a novel decoupling inequality, which may be of independent interest. With this $p$-th moment bound, we show two uniform Hanson-Wright type deviation inequalities for $α$-subexponential entries ($1\le α\le 2$), which recover some known results. As applications, we prove the restricted isometry property of partial random circulant matrices and time-frequency structured random matrices induced by standard $α$-subexponential vectors ($1\le α\le 2$), which extends the previously known results for the subgaussian case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Log-Concave-Tailed Chaoses and the Restricted Isometry Property Dai, Guozheng Su, Zhonggen Ulyanov, Vladimir Wang, Hanchao Probability 60B20, 60G15, 65C50 In this paper, we obtain a $p$-th moment bound for the suprema of a log-concave-tailed nonhomogeneous chaos process, which is optimal in some special cases. A crucial ingredient of the proof is a novel decoupling inequality, which may be of independent interest. With this $p$-th moment bound, we show two uniform Hanson-Wright type deviation inequalities for $α$-subexponential entries ($1\le α\le 2$), which recover some known results. As applications, we prove the restricted isometry property of partial random circulant matrices and time-frequency structured random matrices induced by standard $α$-subexponential vectors ($1\le α\le 2$), which extends the previously known results for the subgaussian case. |
| title | On Log-Concave-Tailed Chaoses and the Restricted Isometry Property |
| topic | Probability 60B20, 60G15, 65C50 |
| url | https://arxiv.org/abs/2401.14860 |