On Mixing Properties of the Limiting Gibbs Process

Source abstract

We consider locally compact second countable Abelian topological group E with Haar measure and pair potentials in E satisfying some natural stability and regularity conditions. We show that the limiting Gibbs process $\operatorname{G}$ with empty boundary conditions is strongly Brillinger-mixing in the spirit of Lothar Heinrich and thereby mixing with respect to the group of translations and ergodic.