Summary
In the random field approach to lattice gas models it has been shown that the one point conditional probabilities determine the finite set conditional probabilities under conditions of strict positivity and regularity. This paper considers the case when strict positivity does not obtain with families of conditional probabilities more general than the one-point conditional probabilities.
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Flood, R.G., Sullivan, W.G. Consistency of random field specifications. Z. Wahrscheinlichkeitstheorie verw Gebiete 53, 147–156 (1980). https://doi.org/10.1007/BF01013312
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DOI: https://doi.org/10.1007/BF01013312