Geodesic
Sufficient conditions for the uniqueness of a probability field and estimates for correlations
Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 609-620.

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In this article we will investigate probability fields (probability distributions) on spaces of the form $X=\prod\limits_{i\in V}X_i$, where $X_i=\{0,1\}$ and $V$ is countable and deduce criteria for the uniqueness of a probability field having a given set of conditional probabilities $$ \{P_i(x_i/X_{V\setminus i})\},\quad i\in V,\quad x_i\in X_i,\quad x_{V\setminus i}\in\prod_{j\in V\setminus i}X_j. $$ The results obtained here are convenient for the estimates of probability fields of a sufficiently general form (e.g., with an arbitrary conjugate potential). In the case of a Markov field an exponential estimate for the correlations is derived. 
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     author = {O. N. Stavskaya},
     title = {Sufficient conditions for the uniqueness of a probability field and estimates for correlations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {609--620},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a14/}
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O. N. Stavskaya. Sufficient conditions for the uniqueness of a probability field and estimates for correlations. Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 609-620. http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a14/