$$p$$-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.
Fields of Study & Subjects
p-Adic Analysis and Mathematical Physics
Stochastic processes and statistical mechanics
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- P-Adic Numbers Ultrametric Analysis and Applications
- Volume
- 18
- Issue
- 1
- Pages
- 62–74
- Publication date
- 1 March 2026
- Language
- EN