On Gibbsianness of Random Fields

S. Dachian, B.S. Nahapetian

2009, v.15, Issue 1, 81-104


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. On the basis of one of the criteria a probabilistically explicit definition of Gibbs random field is given and the development of an alternative approach to the Gibbs theory is started.

Keywords: Gibbsianness,Gibbs random fields,Gibbsian specifications,one-point conditional distribution,one-point finite-conditional distribution


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