On the exponential decay of the n-point correlation functions and the analyticity of the pressure

Abstract

The goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n-point correlation functions for certain unbounded models of Kac type. The methods are based on estimating higher order derivatives of the solution of the Witten Laplacian equation on 1-forms associated with the Hamiltonian of the system. We also provide a formula for the Taylor coefficients of the pressure that is suitable for a direct proof of the analyticity.