Mariya Shcherbina

Characteristic polynomials of non-Hermitian random band matrices

We discuss the asymptotic local behavior of the second correlation functions of the characteristic polynomials of a certain class of Gaussian N x N non-Hermitian random band matrices with a bandwidth W. Given W,N → ∞, we show that this behavior near the point in the bulk of the spectrum exhibits the crossover at W ∼√N: it coincides with those for Ginibre ensemble for W ≫√N, and factorized as 1 ≪ W ≪√N. The behavior of the correlation function near the threshold (W/√N →C) will be also discussed.