p-Adic Markov Chains with Countable State on Trees

Sattarov, I. A.

doi:10.1134/S207004662601005X

p-Adic Markov Chains with Countable State on Trees

2026-03-01

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Sattarov, I. A. *

DOI：10.1134/S207004662601005X

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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.

Keywords:

p-Adic numbers

trees

p-adic Markov chain

Gibbs measures

quasi-phase transition

p-Adic Markov Chains with Countable State on Trees

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