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Open ASEP in the weakly asymmetric regime. (English) Zbl 1410.82014
Summary: We consider ASEP on a bounded interval and on a half-line with sources and sinks. On the full line, L. Bertini and G. Giacomin in [Commun. Math. Phys. 183, No. 3, 571–607 (1997; Zbl 0874.60059)] proved convergence under weakly asymmetric scaling of the height function to the solution of the KPZ equation. We prove here that under similar weakly asymmetric scaling of the sources and sinks as well, the bounded interval ASEP height function converges to the KPZ equation on the unit interval with Neumann boundary conditions on both sides (different parameter for each side), and likewise for the half-line ASEP to KPZ on a half-line. This result can be interpreted as showing that the KPZ equation arises at the triple critical point (maximal current / high density / low density) of the open ASEP.

82C22 Interacting particle systems in time-dependent statistical mechanics
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