U. A. Rozikov, O. N. Khakimov, “$p$-Adic Gibbs measures and Markov random fields on countable graphs”, TMF, 175:1 (2013), 84–92; Theoret. and Math. Phys., 175:1 (2013), 518

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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 175, Number 1, Pages 84–92
DOI: https://doi.org/10.4213/tmf8428 (Mi tmf8428)

This article is cited in 19 scientific papers (total in 19 papers)

p

$p$ -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

Full-text PDF (395 kB) Citations (19)

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DOI: https://doi.org/10.4213/tmf8428

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

$p$ -adic case, the class of

p

$p$ -adic Markov random fields is broader than that of

p

$p$ -adic Gibbs measures. We construct

p

$p$ -adic Markov random fields (on finite graphs) that are not

p

$p$ -adic Gibbs measures. We define a

p

$p$ -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

$p$ -adic probability measures.

Keywords: граф, конфигурация,

p

$p$ -адическая мера Гиббса,

p

$p$ -адические марковские случайные поля.

Received: 16.10.2012

English version:
Theoretical and Mathematical Physics, 2013, Volume 175, Issue 1, Pages 518–525
DOI: https://doi.org/10.1007/s11232-013-0042-0

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: U. A. Rozikov, O. N. Khakimov, “

p

$p$ -Adic Gibbs measures and Markov random fields on countable graphs”, TMF, 175:1 (2013), 84–92; Theoret. and Math. Phys., 175:1 (2013), 518–525

Citation in format AMSBIB

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This publication is cited in the following 19 articles:

M. Alp, Chin Hee Pah, M. K. Saburov, “The description of generalized translation-invariant $p$ -adic Gibbs measures for the Potts model on the Cayley tree of order three”, Theoret. and Math. Phys., 214:3 (2023), 406–420
F. M. Mukhamedov, M. M. Rahmatullaev, A. M. Tukhtabaev, R. Mamadjonov, “The $p$ -adic Ising model in an external field on a Cayley tree: periodic Gibbs measures”, Theoret. and Math. Phys., 216:2 (2023), 1238–1253
Mukhamedov F. Khakimov O., “Translation-Invariant Generalized P-Adic Gibbs Measures For the Ising Model on Cayley Trees”, Math. Meth. Appl. Sci., 44:16 (2021), 12302–12316
Farrukh Mukhamedov, Otabek Khakimov, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, Advances in Non-Archimedean Analysis and Applications, 2021, 115
Ny A.L. Liao L. Rozikov U.A., “P-Adic Boundary Laws and Markov Chains on Trees”, Lett. Math. Phys., 110:10 (2020), 2725–2741
M. A. K. Ahmad, L. Liao, M. Saburov, “Periodic $p$ -adic Gibbs measures of $q$ -state Potts model on Cayley trees I: the chaos implies the vastness of the set of $p$ -adic Gibbs measures”, J. Stat. Phys., 171:6 (2018), 1000–1034
O. N. Khakimov, “ $p$ -Adic solid-on-solid model on a Cayley tree”, Theoret. and Math. Phys., 193:3 (2017), 1880–1893
F. Mukhamedov, O. Khakimov, “On Julia set and chaos in $p$ -adic Ising model on the Cayley tree”, Math. Phys. Anal. Geom., 20:4 (2017), 23
F. Mukhamedov, H. Akin, M. Dogan, “On chaotic behaviour of the $p$ -adic generalized Ising mapping and its application”, J. Differ. Equ. Appl., 23:9 (2017), 1542–1561
M. Saburov, M. A. K. Ahmad, “The dynamics of the Potts-Bethe mapping over $\mathbb{Q}_p$ the case $p \equiv 2 \pmod 3$ ”, 37th International Conference on Quantum Probability and Related Topics (QP37), Journal of Physics Conference Series, 819, ed. L. Accardi, F. Mukhamedov, P. Hee, IOP Publishing Ltd, 2017, UNSP 012017
Zohid T. Tugyonov, “Non uniqueness of $p$ -adic Gibbs distribution for the Ising model on the lattice $Z^d$ ”, Zhurn. SFU. Ser. Matem. i fiz., 9:1 (2016), 123–127
O. N. Khakimov, “A $p$ -adic hard-core model with three states on a Cayley tree”, Siberian Math. J., 57:4 (2016), 726–734
F. Mukhamedov, O. Khakimov, “Phase transition and chaos: $p$ -adic Potts model on a Cayley tree”, Chaos Solitons Fractals, 87 (2016), 190–196
F. Mukhamedov, O. Khakimov, “On periodic Gibbs measures of p-adic Potts model on a Cayley tree”, P-Adic Num Ultrametr Anal Appl, 8:3 (2016), 225
Mansoor Saburov, Mohd Ali Khameini Ahmad, “On Descriptions of All Translation Invariant p-adic Gibbs Measures for the Potts Model on The Cayley Tree of Order Three”, Math Phys Anal Geom, 18:1 (2015)
Farrukh Mukhamedov, Mansoor Saburov, Otabek Khakimov, “Onp-adic Ising–Vannimenus model on an arbitrary order Cayley tree”, J. Stat. Mech., 2015:5 (2015), P05032
O. N. Khakimov, “ $p$ -Adic Gibbs quasimeasures for the Vannimenus model on a Cayley tree”, Theoret. and Math. Phys., 179:1 (2014), 395–404
F. Mukhamedov, “On the strong phase transition for the one-dimensional countable state $p$ -adic Potts model”, J. Stat. Mech.-Theory Exp., 2014, P01007
O. N. Khakimov, “ $p$ -Adic Gibbs measures for the hard core model with three states on the Cayley tree”, Theoret. and Math. Phys., 177:1 (2013), 1339–1351

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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