4 papers · 1 filter
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…