Geodesic
Description of Markovian Random Fields by Gibbsian Conditional Probabilities
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 21-35 
M. B. Averintsev. Description of Markovian Random Fields by Gibbsian Conditional Probabilities. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 21-35. http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a1/
@article{TVP_1972_17_1_a1,
     author = {M. B. Averintsev},
     title = {Description of {Markovian} {Random} {Fields} by {Gibbsian} {Conditional} {Probabilities}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {21--35},
     year = {1972},
     volume = {17},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $T$ be a $v$-dimensional cubic lattice and $L$ a finite set of points from $T$. Suppose that the conditional probabilities of a random field $\xi(t)$ are positive and for any $s\in T$, $x$, $x(t)$. $\Pr\{\xi(s)=x\mid\xi(t)=x(t),\ t\in T\setminus\{s\}\}=\Pr\{\xi(s)=x\mid\xi(t)=x(t),\ t\in L+s\}$ Then $\xi(t)$ is called an $L$-Markov random field with positive conditional probabilities. In the paper, we prove that any such field $\xi(t)$ is a Gibbs field, in general, with many-particle potential.