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

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×n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\times n$$\end{document} matrices in the class considered, we investigate the asymptotic behavior of their empirical spectral distribution as n tends to infinity.