Open ASEP in the Weakly Asymmetric Regime
Open ASEP in the Weakly Asymmetric Regime
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DOI：
10.1002/cpa.21744
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发表时间：
2016-10
影响因子：
3
通讯作者：
Ivan Corwin;Hao Shen
中科院分区：
文献类型：
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作者：
Ivan Corwin;Hao Shen
我们考虑有界区间上的ASEP和具有源和汇的半直线。Bertini和Giacomin在1997年证明了高度函数在弱非对称标度下收敛于KPZ方程的解。我们在这里证明，在源和汇的相似弱非对称标度下，有界区间ASEP高度函数收敛于单位区间上的KPZ方程，两侧具有Neumann边界条件（每一侧的参数不同），半线ASEP收敛于半线上的KPZ方程。这一结果可以解释为表明，KPZ方程出现在三个临界点（最大电流/高密度/低密度）的开放ASEP。© 2018 Wiley Periodicals，Inc.
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.