Guozheng Dai

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20222026

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4 papers · 1 filter

math.PR2024

Quantitative estimates of the singular values of random i.i.d. matrices

Guozheng Dai, Zhonggen Su, Hanchao Wang

Let $M$ be an $n \times n$ random i.i.d. matrix. This paper studies the deviation inequality of $s_{n - k + 1} (M)$ , the $k$ -th smallest singular value of $M$ . In particular, when the en…

math.PR2024

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

Guozheng Dai, Zhonggen Su

This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered $α$ -subexponential entries, $0 < α \leq 1$ . Our method relies up…

math.PR2024

On Log-Concave-Tailed Chaoses and the Restricted Isometry Property

Guozheng Dai, Zhonggen Su, Vladimir Ulyanov +1

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…

math.PR2024

Deviation Inequalities for the Spectral Norm of Structured Random Matrices

Guozheng Dai, Zhonggen Su

We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the $p$ -th moment…

Quantitative estimates of the singular values of random i.i.d. matrices

Uniform Hanson-Wright Type Deviation Inequalities for α-Subexponential Random Vectors

On Log-Concave-Tailed Chaoses and the Restricted Isometry Property

Deviation Inequalities for the Spectral Norm of Structured Random Matrices

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