Abstract
The separation property that characterizes the dynamics of Markov chains is extended to a class of discrete 2D models where the time support, given by the discrete plane Z × Z , is partially ordered by the product of the orderings. The paper analyzes the matrix representation structure of the probability transition map in a 2D Markov chain and some properties of the associated characteristic polynomial in two variables. These allow one to show how the long-term behavior depends on the intersections between the variety of the characteristic polynomial and the distinguished boundary of the unit closed bidisk.
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