Representation of Gibbs fields with Synchronous Random Fields.

We address the issue of the representation of Gibbs random fields over some configuration set by means of synchronous random fields, which lend themselves more efficiently to sampling on parallel devices. After describing the class of synchronous fields which is considered, we introduce a parametrization of synchronous fields by means of a potential. We give conditions under which it is one-to-one, and extend the results to the infinite lattice case. We also prove that every Gibbs field may be represented by such a synchronous field. Keywords. Simulation of random fields, parallel implementation, Gibbs distributions, synchronous distributions. AMS Classification. Primary: 60G60, 60K35, 65Y05. Secondary 60E25, 62F10. 1 Introduction. If S is a finite set of sites, and F a finite set of states, a random field on S with state space F is a probability distribution on the set of all configurations\Omega S = F S . A Gibbs field (or Gibbs distribution) is a random field ß such that ß(x)..