9 papers
A Chaining Approach to Canonical Processes with Log-Concave Tails
Xuanang Hu, Hanchao Wang, Xinglong Wu
We prove a decomposition theorem for canonical processes generated by independent symmetric random variables with log-concave tails, without the condition. The proof uses the…
Rank deficiency of Bernoulli random matrices for growing corank
Zeyan Song, Hanchao Wang
Let A be an n x n Bernoulli random matrix whose entries are i.i.d. Bernoulli(p) random variables. In this paper, we determine the probability that the corank of A is at least k whe…
Failure of Convex-Hull Bounds under Log-Convex Tails
Xuanang Hu, Hanchao Wang
Fix , and let be independent symmetric Weibull random variables, that is, \[ \textsf{P}(|X_i|>t)=e^{-t^r},\qquad t\ge 0. \] We prove that there is no co…
Uniform Concentration for -subexponential Random Operators
Tiankun Diao, Xuanang Hu, Vladimir V. Ulyanov +1
Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on s…
The exact group-sparse recovery for block diagonal matrices with subexponential entries
Guozheng Dai, Tiankun Diao, Hanchao Wang
We study block-diagonal random matrices with i.i.d. subexponential entries and show that, despite their highly structured form, they already guarantee exact sparse recovery from a…
The eigenvalue gap of inhomogeneous symmetric discrete random matrix
Zeyan Song, Hanchao Wang
Let A be an n x n symmetric random matrix whose upper-triangular entries are independent and follow possibly non-identical subgaussian distributions. This paper investigates the sp…
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…
Quantitative estimates of the singular values of random i.i.d. matrices
Guozheng Dai, Zhonggen Su, Hanchao Wang
Let be an random i.i.d. matrix. This paper studies the deviation inequality of , the -th smallest singular value of . In particular, when the en…
On Log-Concave-Tailed Chaoses and the Restricted Isometry Property
Guozheng Dai, Zhonggen Su, Vladimir Ulyanov +1
In this paper, we obtain a -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…