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Open ASEP in the Weakly Asymmetric Regime
Author(s) -
Corwin Ivan,
Shen Hao
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21744
Subject(s) - mathematics , bounded function , scaling , interval (graph theory) , line (geometry) , asymmetric simple exclusion process , mathematical analysis , function (biology) , von neumann architecture , convergence (economics) , neumann boundary condition , boundary (topology) , combinatorics , pure mathematics , geometry , statistics , evolutionary biology , economics , biology , economic growth
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.