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On Gibbsianness of Random Fields

Serguei Dachian·Boris Nahapetian
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Abstract

The problem of characterization of Gibbs random fields is considered. Various Gibbsianness criteria are obtained using the earlier developed one-point framework which in particular allows to describe random fields by means of either one-point conditional or one-point finite-conditional distributions. The main outcome are the criteria in terms of one-point finite-conditional distribution, one of which can be taken as a purely probabilistic definition of Gibbs random field.

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Serguei Dachian, Boris Nahapetian. 2006-09-25. On Gibbsianness of Random Fields. https://arxiv.org/abs/math/0609688

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