Open ASEP in the Weakly Asymmetric Regime

Ivan Corwin Columbia University Hao Shen Columbia University

Probability mathscidoc:1805.28006

Communications on Pure and Applied Mathematics, 2018
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.
Stochastic PDE, KPZ equation, interacting particle system
[ Download ] [ 2018-05-30 09:03:04 uploaded by haoshen ] [ 687 downloads ] [ 0 comments ]
@inproceedings{ivan2018open,
  title={Open ASEP in the Weakly Asymmetric Regime},
  author={Ivan Corwin, and Hao Shen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180530090304342674093},
  booktitle={Communications on Pure and Applied Mathematics},
  year={2018},
}
Ivan Corwin, and Hao Shen. Open ASEP in the Weakly Asymmetric Regime. 2018. In Communications on Pure and Applied Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180530090304342674093.
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