4 years ago

The KPZ Limit of ASEP with Boundary.

Shalin Parekh

It was recently proved in [Corwin-Shen, 2016] that under weak asymmetry scaling, the height functions for open ASEP on the half-line and on a bounded interval converge to the Hopf-Cole solution of the KPZ equation with Neumann boundary conditions. In their assumptions [Corwin-Shen, 2016] chose positive values for the Neumann boundary conditions, and they assumed initial data which is close to stationarity. By developing more extensive heat-kernel estimates, we extend their results to negative values of the Neumann boundary parameters, and we also show how to generalize their results to narrow-wedge initial data (which is very far from stationarity). As a corollary via [Barraquand-Borodin-Corwin-Wheeler, 2017], we obtain the Laplace transform of the one-point distribution for half-line KPZ, and use this to prove $t^{1/3}$-scale GOE Tracy-Widom long-time fluctuations.

Publisher URL: http://arxiv.org/abs/1711.05297

DOI: arXiv:1711.05297v1

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