Statistical behavior of the characteristic polynomials of a family of pseudo-Hermitian Gaussian matrices

Abstract

In this paper, we extend previous studies conducted by the authors in a family of pseudo-Hermitian Gaussian matrices. Namely, we further the studies of the two pseudo-Hermitian random matrix cases previously considered, the first of a matrix of order N with two interacting blocks of sizes M and N − M and the second of a chessboard-like structured matrix of order N whose subdiagonals alternate between Hermiticity and pseudo-Hermiticity. Following an average characteristic polynomial approach, we obtain sequences of polynomials whose roots describe the average value of the polynomials of the matrices of the family at hand, for each case considered. We also present numerical results regarding the statistical behavior of the average characteristic polynomial, and contrast that to the spectral behavior of sample matrices of this family.