A THEOREM ABOUT RANDOM FIELDS

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Determinantal Point Processes for Machine Learning (2012, background): “The converse also holds: any distribution that is Markov with respect to G, as long as it is strictly positive, can be decomposed over the cliques of G as in Equation (88) [Grimmett, 1973].”
Markov properties for mixed graphs (2011, unknown): “Alternative proofs were later given independently by several authors, for example [12; 3]; see also [4].”
Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “Moreover, by the Hammersley-Clifford theorem [103, 23, 99], the precision matrix P has the same sparsity pattern as the graph adjacency matrix (i.”
Spatial Interaction and the Statistical Analysis of Lattice Systems (1974, background): “Finally, we note that, for discrete variables, a further proof of the HammersleyClifford theorem has been given by Grimmett (1973).”