Comets, Francis 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 C. R. Acad. Sci., Paris, Sér. I 303, 511-513 (1986). 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. Cited in 2 ReviewsCited in 23 Documents MSC: 60F10 Large deviations 60G60 Random fields 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:large deviations principle; stationary Gibbsian fields; Gibbs variational formula PDFBibTeX XMLCite \textit{F. Comets}, C. R. Acad. Sci., Paris, Sér. I 303, 511--513 (1986; Zbl 0606.60035)