KPZ equation from ASEP plus general speed-change drift

Kevin Yang

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arXiv · 2409.10513

KPZ equation from ASEP plus general speed-change drift

Kevin Yang

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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.

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Kevin Yang. 2024-09-16. KPZ equation from ASEP plus general speed-change drift. https://arxiv.org/abs/2409.10513

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