On Gibbsianness of Random Fields
Résumé
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 which a simple and comprehensible definition of Gibbs random field is given.