Exact solution for the stationary Kardar-Parisi-Zhang equation
Takashi Imamura, Tomohiro Sasamoto
TL;DR
This paper presents the first exact solution for the stationary one-dimensional KPZ equation, providing explicit formulas for height distribution and two-point correlation functions valid at any finite time.
Contribution
It introduces a novel exact solution for the stationary KPZ equation, including formulas for height distribution and correlations, enabling precise numerical evaluation.
Findings
Exact formula for height distribution in stationary KPZ
Explicit expression for stationary two-point correlation function
Solution valid for any finite time t
Abstract
We obtain the first exact solution for the stationary one-dimensional Kardar-Parisi-Zhang equation. A formula for the distribution of the height is given in terms of a Fredholm determinant, which is valid for any finite time . The expression is explicit and compact enough so that it can be evaluated numerically. Furthermore, by extending the same scheme, we find an exact formula for the stationary two-point correlation function.
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