报告题目：Sparse Hanson-Wright Inequalities

报告人： 何奕昀  University of California, San Diego

报告时间：9月2日 10:00-11:00

报告地点：五教5106  

摘要：

We derive new Hanson-Wright-type inequalities tailored to the quadratic forms of random vectors with sparse independent components. Specifically, we consider cases where the components of the random vector are sparse α-subexponential random variables with α>0. When α=∞, these inequalities can be seen as quadratic generalizations of the classical Bernstein and Bennett inequalities for sparse bounded random vectors. To establish this quadratic generalization, we also develop new Bersntein-type and Bennett-type inequalities for linear forms of sparse α-subexponential random variables that go beyond the bounded case (α=∞). Our proof relies on a novel combinatorial method for estimating the moments of both random linear forms and quadratic forms.