Erdős-Rényi laws for Gibbs measures (Q1328204)

Definitions of Gibbs measures are given and their large deviation properties are recalled. For a general random field obeying a large deviation principle with uniformity in the lower bound, the Erdős- Rényi law is proved at the level of the empirical field. The result also applies to hypermixing processes. Some other problems are considered related to large deviations for Gibbs measures.