Eigenvectors and ratio limit theorems for Markov chains and their relatives (Q1808872)

The paper is a survey of a class of discrete Markov chains, described by column-finite infinite matrices. It is considered a finite subset of states, which is a dimension group, and the study of the nonnegative eigenvectors is equivalent to the traces on an analytic one parameter family of dimension groups. Some sufficient conditions which assure the existence of at most one nonnegative eigenvector per eigenvalue are given. A ratio limit theorem is proved if it is supposed that there exists just one nonnegative eigenvector for the spectral radius.