On the correlations of some microscopic random systems

Abstract

We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be written in terms of the generator of a two-dimensional random walk, whose jump rates are model dependent. From this, we deduce an asymptotic independence which is shared by many models.

24 pages, 2 figures