98-193 Redig F.,Maes C., Van Moffaert A.

Almost Gibbsian versus Weakly Gibbsian measures (355K, Postscript) Mar 13, 98

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Abstract. We consider various extensions of the standard definition of Gibbs states for lattice spin systems. When a random field has conditional distributions which are almost surely continuous (almost Gibbsian field), then there is a potential for that field which is almost surely summable (weakly Gibbsian field). This generalizes the standard Kozlov-Sullivan theorems. The converse is not true in general. We give (counter)examples illustrating the relation between topological and measure-theoretic aspects of generalized Gibbs definitions.

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