Multilevel limits of spiked random matrix corners processes

Abstract

We consider the largest eigenvalues of submatrices of the classical Gaussian random matrices with a finite rank spike in the critical BBP regime. We show that they converge to a multilevel interlacing particle system whose lowest level is the Airy${}_{\beta }$ point process. Our construction and scaling limits extend in a natural way to non-classical $\beta >0$.

v2: revisions, new title