Coupling independent walkers and the inclusion process

TL;DR

This paper proves local equilibrium propagation and steady state properties of the symmetric inclusion process using self-duality and a novel coupling with independent random walkers, advancing understanding of interacting particle systems.

Contribution

It introduces a coupling method between SIP particles and independent walkers, enabling analysis of local equilibrium and steady states.

Findings

Propagation of local equilibrium established

Local equilibrium in non-equilibrium steady state demonstrated

Coupling technique with independent walkers developed

Abstract

We show propagation of local equilibrium for the symmetric inclusion process (SIP) after diffusive rescaling of space and time, as well as the local equilibrium property of the non-equilibrium steady state in the boundary driven SIP. The main tool is self-duality and a coupling between $n$ SIP particles and $n$ independent random walkers.