Ergodic properties of the harmonic process

TL;DR

This paper investigates the fluctuation properties of a boundary driven harmonic model's non-equilibrium steady state, providing law of large numbers, CLT, and large deviation results.

Contribution

It offers detailed fluctuation analysis and quantitative deviation results for a class of non-equilibrium steady states, extending understanding of harmonic models.

Findings

Proved law of large numbers for the model

Established central limit theorem for local functions

Derived large deviation principles and deviation estimates

Abstract

In this paper we study detailed fluctuation results for a class of non-equilibrium steady states. The main example is the boundary driven harmonic model \cite{frassek2022exact}. In this model, the non-equilibrium steady state (NESS) is a mixture of products of geometric distributions, of which the local parameters are in turn distributed as uniform order statistics. For such a NESS, we prove law of large numbers, central limit theorem and large deviation results for fields of a general local functions (generalizing the density field). We also obtain quantitative results on the deviation from local equilibrium.