Jacobi matrices on trees generated by Angelesco systems: Asymptotics of coefficients and essential spectrum

Abstract

We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was recently discovered. In this paper, we consider Angelesco systems formed by two analytic weights and obtain asymptotics of the recurrence coefficients and strong asymptotics of MOPs along all directions (including the marginal ones). These results are then applied to show that the essential spectrum of the related Jacobi matrix is the union of intervals of orthogonality.