Uniform Hanson-Wright Type Deviation Inequalities for $\alpha$-Subexponential Random Vectors

Guozheng Dai; Zhonggen Su

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arXiv · 2405.07207

Uniform Hanson-Wright Type Deviation Inequalities for $\alpha$-Subexponential Random Vectors

Guozheng Dai·Zhonggen Su

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Abstract

This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered $\alpha$-subexponential entries, $0<\alpha\le 1$. Our method relies upon a novel decoupling inequality and a comparison of weak and strong moments. As an application, we use the derived inequality to prove the restricted isometry property of partial random circulant matrices generated by standard $\alpha$-subexponential random vectors, $0<\alpha\le 1$.

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Guozheng Dai, Zhonggen Su. 2024-05-12. Uniform Hanson-Wright Type Deviation Inequalities for $\alpha$-Subexponential Random Vectors. https://arxiv.org/abs/2405.07207

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