Guozheng Dai

activity

20222026

collaborators

10 papers

math.PR2026

Concentration of bounded sparse chaoses and sparse Khatri-Rao embeddings

Guozheng Dai, Yiyun He, Ke Wang +1

We establish moment and mixed-tail inequalities for fixed-order decoupled homogeneous chaoses generated by independent, centered, sparse bounded random variables. Our bounds apply…

math.PR2026

Sparsity-adaptive concentration inequalities for random polynomials

Guozheng Dai, Ke Wang

We prove concentration inequalities for polynomials of independent, sparse $α$ -sub-exponential random variables. Specifically, we consider $X_{i} = δ_{i} ξ_{i}$ , where the Bernoulli selecto…

math.PR2025

A note on the improved sparse Hanson-Wright inequalities

Guozheng Dai, Yiyun He, Ke Wang +1

We establish sparse Hanson-Wright inequalities for quadratic forms of sparse $α$ -sub-exponential random vectors with exponent parameter $α \in (0, 2]$ . In the regime $0 < α \leq 1$ we d…

math.PR2025

The Rank and Singular Values of the Inhomogeneous Subgaussian Random Matrices

Guozheng Dai, Zeyan Song, Hanchao Wang

Let A be an n*n random matrix with mean zero and independent inhomogeneous non-constant subgaussian entries. We get that for any k<c\sqrt{n}, the probability of the matrix has a lo…

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…

math.PR2023

Quantitative estimates of the spectral norm of random matrices with independent columns

Guozheng Dai, Zhonggen Su, Hanchao Wang

This paper investigates the nonasymptotic properties of the spectral norm of some random matrices with independent columns. In particular, we consider an $m \times n$ random matrix…

math.PR2022

Tail Bounds on the Spectral Norm of Sub-Exponential Random Matrices

Guozheng Dai, Zhonggen Su, Hanchao Wang

Let $X$ be an $n \times n$ symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of $X$ with Gaussian ent…

Concentration of bounded sparse chaoses and sparse Khatri-Rao embeddings

Sparsity-adaptive concentration inequalities for random polynomials

A note on the improved sparse Hanson-Wright inequalities

The Rank and Singular Values of the Inhomogeneous Subgaussian Random Matrices

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

Quantitative estimates of the spectral norm of random matrices with independent columns

Tail Bounds on the Spectral Norm of Sub-Exponential Random Matrices

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