Phase transition for the bottom singular vector of rectangular random matrices

Mathphys Analysis Seminar

In physics, the phase transition between localized and delocalized phases in disordered systems, often called the Anderson transition, has attracted significant interest. Several intriguing models display this behavior, including random Schrdinger operators, random band matrices, and sparse random matrices. Heavy-tailed random matrices similarly capture this phase transition, making them a crucial class of models in understanding localization phenomena. In this talk, we will discuss the phase transition of the right singular vector associated with the smallest singular value of a rectangular random matrix. This work is in collaboration with Zhigang Bao (University of Hong Kong) and Xiaocong Xu (University of Southern California).