Finite-Rank Complex Deformations of Random Band Matrices: Sigma-Model Approximation

We study the distribution of complex eigenvalues z1, ... , zN of random Hermitian N x N block band matrices with a complex deformation of a finite rank. Assuming that the width of the band W grows faster than v/N, we proved that the limiting density of sz1, ... , szN in a sigma-model approximation coincides with that for the Gaussian Unitary Ensemble. The method follows the techniques of [16].