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Grandes déviations pour des champs de Gibbs sur \({\mathbb{Z}}^ d\). (Large deviations results for Gibbsian random fields on \({\mathbb{Z}}^ d)\). (French) Zbl 0606.60035

A large deviations principle is first proved for the empirical process of i.i.d. random variables indexed by the integer lattice \({\mathbb{Z}}^ d\), \(d\geq 1\). This result is then extended to stationary Gibbsian fields corresponding to a summable interaction, and we obtain the Gibbs variational formula.

MSC:

60F10 Large deviations
60G60 Random fields
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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