Witten Laplacian Methods for the Decay of Correlations

Abstract

The aim of this paper is to apply direct methods to the study of integrals that appear naturally in Statistical Mechanics and Euclidean Field Theory. We provide weighted estimates leading to the exponential decay of the two-point correlation functions for certain classical convex unbounded models. The methods involve the study of the solutions of the Witten Laplacian equations associated with the Hamiltonian of the system.