Quadratic form of heavy-tailed self-normalized random vector with applications in $\alpha$-heavy Marčenko--Pastur law

Zhaorui Dong, Johannes Heiny, Jianfeng Yao

Let $\mathbf{x}$ be a random vector with $n$ i.i.d.\ real-valued components in the domain attraction of an $\alpha$-stable law with $\alpha \in (0,2)$, and let $\mathbf{y}=\mathbf{x}/\|\mathbf…