Multilinearity of two-point correlation functions in one-dimensional models out of equilibrium

TL;DR

This paper investigates conditions under which two-point correlation functions in one-dimensional non-equilibrium models are multilinear, highlighting the first example of such behavior without product stationary measures.

Contribution

It provides necessary and sufficient conditions for multilinearity of two-point functions based on first two moments and redistribution parameters.

Findings

Identifies conditions for multilinear two-point functions

First example of multilinearity without product measures

Connects correlation structure to reservoir moments

Abstract

In this note we consider non-equilibrium steady states of one-dimensional models of heat conduction (wealth exchange) which are coupled to some reservoirs creating currents. In particular we will give sufficient and necessary conditions which will depend only on the first two moments of the reservoir measures and the redistribution parameter under which the two-point functions are multilinear. This presents the first example of multilinear two-point functions in the absence of product stationary measures.