BBP phenomena for deformed random band matrices

Abstract

We study additive finite-rank perturbations of random periodic band matrices under the assumption that the nontrivial eigenvalues of the perturbation do not depend on the dimension. We establish the eigenvalue/eigenvector BBP transition in this model for band widths $b_N\gg N^{\epsilon }$. Our analysis relies on moment method calculations for general vector states.

25 pages, 1 figure