Weakly coupled Gibbs measures

Summary We formulate an abstract functional-analytic framework for the study of Gibbs measures on infinite product spaces. Working in this frame-work, we present a detailed analysis of the weak-coupling regime. Specifically, we derive general theorems on existence of the Gibbs measure, analyticity in its component Gibbs factors, and exponential decay of correlations and truncated expectations in the spread of distant families of random variables. In translation-invariant situations we obtain a central limit theorem. Our main tool is a series expansion in truncated expectations, which we analyze with L^p methods.Original title: Analyticity and Decay of Correlations in Weakly Coupled Lattice Models.Supported by N.S.F. Grant PHY76-17191Dedicated to Professor Leopold Schmetterer