# Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line

@article{Krajenbrink2019ReplicaBA,
title={Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line},
author={Alexandre Krajenbrink and Pierre Le Doussal},
journal={arXiv: Statistical Mechanics},
year={2019}
}
• Published 2019
• Physics, Mathematics
• arXiv: Statistical Mechanics
We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at $x=0$ either repulsive $A>0$, or attractive $A - \frac{1}{2}$ the large time PDF is the GSE Tracy-Widom distribution. For $A= \frac{1}{2}$, the critical point at which the DP binds to the wall, we… Expand
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