# Stationary Correlations for the 1D KPZ Equation

@article{Imamura2013StationaryCF,
title={Stationary Correlations for the 1D KPZ Equation},
author={Takashi Imamura and Tomohiro Sasamoto},
journal={Journal of Statistical Physics},
year={2013},
volume={150},
pages={908-939}
}
• Published 16 October 2012
• Mathematics
• Journal of Statistical Physics
We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit…
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Reflected Brownian Motions in the KPZ Universality Class
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