Characteristic Polynomials for Random Band Matrices Near the Threshold.

The paper continues (Shcherbina and Shcherbina in Commun Math Phys 351:1009–1044, 2017); Shcherbina in Commun Math Phys 328:45–82, 2014) which study the behaviour of second correlation function of characteristic polynomials of the special case of n × n one-dimensional Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J = (- W 2 ▵ + 1) - 1 . Applying the transfer matrix approach, we study the case when the bandwidth W is proportional to the threshold n . [ABSTRACT FROM AUTHOR]