Geodesic
$p$-Adic Gibbs measures and Markov random fields on countable graphs
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 1, pp. 84-92

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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.
Mots-clés : граф, конфигурация, $p$-адическая мера Гиббса, $p$-адические марковские случайные поля. 
@article{TMF_2013_175_1_a5,
     author = {U. A. Rozikov and O. N. Khakimov},
     title = {$p${-Adic} {Gibbs} measures and {Markov} random fields on countable graphs},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {84--92},
     publisher = {mathdoc},
     volume = {175},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_1_a5/}
}
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U. A. Rozikov; O. N. Khakimov. $p$-Adic Gibbs measures and Markov random fields on countable graphs. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 1, pp. 84-92. http://geodesic.mathdoc.fr/item/TMF_2013_175_1_a5/