Concentration Inequalities for Sub-Weibull Random Tensors

Yunfan Zhao

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arXiv · 2509.03439

Concentration Inequalities for Sub-Weibull Random Tensors

Yunfan Zhao

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Abstract

We extend the theory of concentration inequalities to simple random tensors with heavy-tailed coefficients. Specifically, we consider the class of sub-Weibull distributions $\mathcal{S}_\alpha$ for $\alpha \in [1, 2]$. 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.

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Yunfan Zhao. 2025-09-03. Concentration Inequalities for Sub-Weibull Random Tensors. https://arxiv.org/abs/2509.03439

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