$$p$$-Adic Markov Chains with Countable State on Trees

Abstract

In this paper, we investigate spin systems on general infinite trees. The spins can take countably many values, and nearest-neighbor interactions are governed by a $$p$$ -adic stochastic matrix. We establish sufficient conditions on the stochastic matrix that guarantee the uniqueness of the associated Markov chain. Furthermore, we identify a family of stochastic matrices that lead to the existence of at least two distinct $$p$$ -adic Markov chains on an infinite tree, particularly a Cayley tree.

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Identifiers

DOI

10.1134/s207004662601005x

Citations and references