Concentration Inequalities for Sub-Weibull Random Tensors
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911499844321280 |
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| author | Zhao, Yunfan |
| author_facet | Zhao, Yunfan |
| contents | We extend the theory of concentration inequalities to simple random tensors with heavy-tailed coefficients. Specifically, we consider the class of sub-Weibull distributions $\mathcal{S}_α$ for $α\in [1, 2]$. We establish concentration bounds for Euclidean functions of such tensors, exhibiting a phase transition between sub-gaussian and heavy-tailed regimes. Our results rely on a new Generalized Maximal Inequality for products of heavy-tailed random variables and a martingale analysis using Nagaev-type inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration Inequalities for Sub-Weibull Random Tensors Zhao, Yunfan Mathematical Finance Probability Primary 60E15, Secondary 60F10, 60B20, 15A69 We extend the theory of concentration inequalities to simple random tensors with heavy-tailed coefficients. Specifically, we consider the class of sub-Weibull distributions $\mathcal{S}_α$ for $α\in [1, 2]$. We establish concentration bounds for Euclidean functions of such tensors, exhibiting a phase transition between sub-gaussian and heavy-tailed regimes. Our results rely on a new Generalized Maximal Inequality for products of heavy-tailed random variables and a martingale analysis using Nagaev-type inequalities. |
| title | Concentration Inequalities for Sub-Weibull Random Tensors |
| topic | Mathematical Finance Probability Primary 60E15, Secondary 60F10, 60B20, 15A69 |
| url | https://arxiv.org/abs/2509.03439 |