On Gibbsianness of Random Fields

Serguei Dachian (1) , Boris Nahapetian (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 IMNASA - Institute of Mathematics

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.

Mots clés: Gibbsianness; Gibbs random fields; Gibbsian specifications; one-point conditional distribution; one-point finite-conditional distribution

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Serguei Dachian, Boris Nahapetian. On Gibbsianness of Random Fields. Markov Processes And Related Fields, 2009, 15 (1), pp.81-104. ⟨hal-00098282v2⟩