Eigenvectors and ratio limit theorems for Markov chains and their relatives
 David E. Handelman
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Associated to classes of countable discrete Markov chains or, more generally, columnfinite nonnegative infinite matrices, and a finite subset of the state space, is a dimension group. In many cases, this dimension group gives information about the nonnegative eigenvectors of the process. Moreover, the study of the nonnegative eigenvectors is, equivalent to the traces on an analytic one parameter family of dimension groups. We pay particular attention to the case that there is at most one nonnegative eigenvector per eigenvalue, giving a number of sufficient conditions. Using the techniques developed here, we also show that under a reasonable set of conditions (principle among them that there be just one nonnegative eigenvector for the spectral radius), a (onesided) ratio limit theorem holds.
 Title
 Eigenvectors and ratio limit theorems for Markov chains and their relatives
 Journal

Journal d’Analyse Mathématique
Volume 78, Issue 1 , pp 61116
 Cover Date
 199912
 DOI
 10.1007/BF02791129
 Print ISSN
 00217670
 Online ISSN
 15658538
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Authors

 David E. Handelman ^{(1)}
 Author Affiliations

 1. Mathematics Department, University of Ottawa, K1N 6N5, Ottawa, ON, Canada