Gibbs fields

Abstract

We begin in § 2.2.1. with Dobrushin theory for random fields defined through conditional marginal distributions. The comparison result of § 2.2.1.1. yields Dobrushin’s uniqueness condition (§ 2.2.1.2.) and then a mixing condition arises in § 2.2.1.3. The fundamental example of such random fields is the Markov field case (§ 2.2.2.), it is described in terms of potentials in § 2.2.2.1. The non compact case is evocated in § 2.2.3. with the examples of point processes in § 2.2.3.1 and diffusion based random fields in § 2.2.3.2.