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Concentration Inequalities for Sub-Weibull Random Tensors

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  • Yunfan Zhao

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.

Suggested Citation

  • Yunfan Zhao, 2025. "Concentration Inequalities for Sub-Weibull Random Tensors," Papers 2509.03439, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2509.03439
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    File URL: http://arxiv.org/pdf/2509.03439
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