Large Deviations for Random Fields on $Z^d$ with Unbounded Interaction

T. Kuneth

2004, v.10, №2, 249-288

ABSTRACT

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

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