Characteristic Polynomials of Random Banded Hessenberg Matrices and Hermite–Padé Approximation

Abstract

We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries belonging to different diagonals. For a sequence of \(n\times n\) matrices in the class considered, we investigate the asymptotic behavior of their empirical spectral distribution as n tends to infinity.