L. A. Bunimovich and B. Z. Webb developed a theory for transforming a finite weighted graph while preserving its spectrum, referred as isospectral reduction theory. In this workwe extend this theory to a class of operators on Banach spaces that include Markov type operators. We apply this theory to infinite countable weighted graphs admitting a finite structural set to calculate the stationary measures of a family of countable Markov chains.
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Pedro Duarte, Maria Joana Torres, Isospectral reduction in infinite graphs. J. Spectr. Theory 10 (2020), no. 3, pp. 955–989DOI 10.4171/JST/318