Macroscopic stability for nonfinite range kernels

TL;DR

This paper extends macroscopic stability results from finite-range to nonfinite-range kernels in one-dimensional conservative attractive models, broadening the scope of hydrodynamics applications.

Contribution

It generalizes the strong macroscopic stability framework to include models with nonfinite range kernels, including misanthrope processes.

Findings

Extended macroscopic stability to nonfinite range kernels

Broadened hydrodynamics applicability to more models

Included misanthrope processes in the analysis

Abstract

We extend the strong macroscopic stability introduced in Bramson & Mountford (2002) for one-dimensional asymmetric exclusion processes with finite range to a large class of one-dimensional conservative attractive models (including misanthrope process) for which we relax the requirement of finite range kernels. A key motivation is extension of constructive hydrodynamics result of Bahadoran et al. (2002, 2006, 2008) to nonfinite range kernels.