Large Deviations for Random Fields on $Z^d$ with Unbounded Interaction
2004, v.10, Issue 2, 249-288
We prove a Large Deviation Principle (LDP) for the empirical fields of Gibbs random fields with arbitrary state space. The stationary manybody interaction $\varphi$ may be unbounded, but must satisfy strong regularity and stability conditions. The underlying topology on the set of all stationary probability measures is defined by the local functions with a suitable growth condition. Along the way we prove existence and various properties of specific energy and entropy.
Keywords: large deviations,Gibbs fields,unbounded interaction