Open ASEP in the Weakly Asymmetric Regime. Issue 10 (16th February 2018)

• Record Type: Journal Article
• Authors: Corwin, Ivan; Shen, Hao
• Is Part Of: Communications on pure and applied mathematics. Volume 71:Issue 10(2018:Oct.)
• Page Start: 2065
• Page End: 2128
• Publication Date: 2018-02-16
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21744
• Languages: English
• ISSNs: 0010-3640

Abstract

Abstract: We consider ASEP on a bounded interval and on a half‐line with sources and sinks. On the full line, Bertini and Giacomin in 1997 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. © 2018 Wiley Periodicals, Inc.