This article is cited in 21 papers

$p$-Adic Gibbs measures and Markov random fields on countable graphs

U. A. Rozikov, O. N. Khakimov

Институт математики при Национальном университете Узбекистана им. М. Улугбека, Ташкент, Узбекистан

Abstract: The notions of the Gibbs measure and of the Markov random field are known to coincide in the real case. But in the $p$-adic case, the class of $p$-adic Markov random fields is broader than that of $p$-adic Gibbs measures. We construct $p$-adic Markov random fields (on finite graphs) that are not $p$-adic Gibbs measures. We define a $p$-adic Markov random field on countable graphs and show that the set of such fields is a nonempty closed subspace in the set of all $p$-adic probability measures.

Keywords: граф, конфигурация, $p$-адическая мера Гиббса, $p$-адические марковские случайные поля.

Received: 16.10.2012

DOI: 10.4213/tmf8428

 English version: Theoretical and Mathematical Physics, 2013, 175:1, 518–525

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