Markov fields with polygonal realizations

Abstract

We define a new class of Markov random fields with two-dimensional parameter z∈T⊂ℝ2, which take a finite number of values separated by random polygonal boundaries. In some special cases, these random fields are consistent in T and allow and alternative description in terms of the equilibrium evolution of a system of one-dimensional particles. © 1989 Springer-Verlag.