Markov fields with polygonal realizations (Q1099510)

We define a new class of Markov random fields with two-dimensional parameter \(z\in T\subset {\mathbb{R}}^ 2,\) 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 an alternative description in terms of the equilibrium evolution of a system of one- dimensional particles.