Gibbsian Characterization for the Reversible Measures of Interacting Particle Systems
2009, v.15, №4, 441-476
For a large class of interacting particle systems (IPS) on the d-dimensional square lattice a criterion for reversibility of measures is derived. It is shown that a reversible measure exists if and only if the local processes which the IPS consists of are reversible w.r.t. the same measure. This result is translated into constraints that are put on the family of conditional probabilities of the reversible measure. For spin processes as well as more complex composite IPS a necessary and sufficient condition for the existence of reversible measures is proven and it is shown that the reversible measures coincide with the Gibbs measures corresponding to a specification that is constructed directly from the transition rates.
Keywords: reversible interacting particle system,Gibbs measure,detailed balance condition,spin process