Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion

TL;DR

This paper investigates the hydrodynamic behavior of a symmetric exclusion process with long-range jumps and boundary reservoirs, revealing how super-diffusive operators and boundary conditions influence the macroscopic equations.

Contribution

It provides a detailed analysis of the hydrodynamic limit for a super-diffusive exclusion process with boundary effects, extending previous results and characterizing the resulting fractional PDEs.

Findings

Hydrodynamic equations involve regional fractional Laplacians with boundary conditions.

The model exhibits super-diffusive behavior due to heavy-tailed jumps.

The work addresses open questions from prior research on similar models.

Abstract

We study the hydrodynamic limit for a model of symmetric exclusion processes with heavy-tailed long jumps and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators that are given by the regional fractional Laplacian with some additional reaction terms and various boundary conditions. This work solves some questions left open in \cite{BJGO2} about the same model.