Microscopic stationary states for stochastic systems with particle flux (Q1093266)

Let \(\eta _ t\) be the symmetric nearest neighbor simple exclusion process on \({\mathbb{Z}}^ 3\) modified to allow the spontaneous creation and destruction of particles at the origin. We study the invariant measures for the system in this non-equilibrium situation, for which a net current of particles flows from the origin. We analyze the n-point correlations of the invariant measures, which for \(n=2\) behave like \(\max (x_ 1,x_ 2)^{-4}\).