KPZ equation from ASEP plus general speed-change drift
Probability
2024-12-11 v5
Abstract
We derive the KPZ equation as a continuum limit of height functions in asymmetric simple exclusion processes with drift that depends on the local particle configuration. To our knowledge, it is a first such result for a class of particle systems without duality or explicit invariant measures. The tools developed in this paper consist of estimates on the corresponding Kolmogorov equations, giving a more robust proof of the Boltzmann-Gibbs principle. These tools are not exclusive to KPZ.
Cite
@article{arxiv.2409.10513,
title = {KPZ equation from ASEP plus general speed-change drift},
author = {Kevin Yang},
journal= {arXiv preprint arXiv:2409.10513},
year = {2024}
}
Comments
Revised abstract and introduction, proof-read version