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.
@article{MZM_1975_18_4_a14,
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/}
}
TY - JOUR AU - O. N. Stavskaya TI - Sufficient conditions for the uniqueness of a probability field and estimates for correlations JO - Matematičeskie zametki PY - 1975 SP - 609 EP - 620 VL - 18 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a14/ LA - ru ID - MZM_1975_18_4_a14 ER -
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/