Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices

Abstract

Asymptotic results for the Perron-Frobenius eigenvalue of a nonnegative Hessenberg-Toeplitz matrix as the dimension of the matrix tends to 8 are given. The results are used and interpreted in terms of source entropies in the case where the Hessenberg-Toeplitz matrix arises as the transition matrix of a finite-state machine generating certain constrained sequences of ±1's