Periodic points of a p-adic operator and their p-adic Gibbs measures

2022/07/10 by U. A. Rozikov, Rozikov, U. A., I. A. Sattarov +3 · 1 citation
Computer Science · Mathematics · #82B26 (12J12 46S10 60K35) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2207.04379

openalex publication_date 2022/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we investigate generalized Gibbs measure (GGM) for p-adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order k≥ 2. This model is defined by p-adic parameters λ_i, i∈ \mathbb N. We analyze p-adic functional equation which provides the consistency condition for the finite-dimensional generalized Gibbs distributions. Each solutions of the functional equation defines a GGM by p-adic version of Kolmogorov's theorem. We define p-adic Gibbs distributions as limit of the consistent family of finite-dimensional generalized Gibbs distributions and show that, for our p-adic HC model on a Cayley tree, such a Gibbs distribution does not exist. Under some conditions on parameters p, k and λ_i we find the number of translation-invariant and two-periodic GGMs for the p-adic HC model on the Cayley tree of order two.

Cited by

• p-adic dynamical systems for p-adic λ-models on the Cayley trees

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