Non-equilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps

TL;DR

This paper establishes a scaling limit for a tagged particle in a long-jump exclusion process, showing it converges to a time-inhomogeneous process linked to a fractional heat equation, extending understanding of non-equilibrium dynamics.

Contribution

It introduces a new invariance principle for tagged particles in long-jump exclusion processes out of equilibrium, connecting microscopic dynamics to fractional PDEs.

Findings

Tagged particle converges to a process with independent increments.

Limit process is related to a fractional heat equation.

Results extend non-equilibrium scaling limits to long-jump interactions.

Abstract

We prove an invariance principle for a tagged particle in a simple exclusion process out of equilibrium. The scaling limit is a time-inhomogeneous process of independent increments, related to the solution of a fractional heat equation.