We obtain Hanson-Wright inequalities for the quadratic form of a random vector with independent sparse random variables. Specifically, we consider cases where the components of the random vector are sparse $\alpha$-sub-exponential random variables with $\alpha>0$. Our proof relies on a novel combinatorial approach to estimate the moments of the random quadratic form.

翻译：我们针对具有独立稀疏随机变量的随机向量的二次型，获得了 Hanson-Wright 不等式。具体而言，我们考虑随机向量的分量是稀疏的 $\alpha$-次指数随机变量，其中 $\alpha>0$。我们的证明依赖于一种新颖的组合方法来估计随机二次型的矩。