Phase transition for the bottom singular vector of rectangular random matrices

Zhigang Bao, Jaehun Lee, Xiaocong Xu

In this paper, we consider the rectangular random matrix $X=(x_{ij})\in {\mathbb{R}}^{N\times n}$ whose entries are iid with tail $\mathbb{P}(|x_{ij}|>t)\sim t^{-\hat{I}\pm }$ for some $\hat{I}\pm >0$…