Open ASEP height functions with general local boundary asymmetries converge to the open KPZ equation without Liggett's condition or explicit invariant measures.
KPZ equation from ASEP plus general speed-change drift
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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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KPZ equation from open ASEP with general boundary asymmetry
Open ASEP height functions with general local boundary asymmetries converge to the open KPZ equation without Liggett's condition or explicit invariant measures.