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Exact solution for the stationary Kardar-Parisi-Zhang equation

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 $t$. 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.

preprint2012arXivOpen access
Takashi ImamuraTomohiro Sasamoto
cond-mat.stat-mechmath-phmath.MP
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Takashi ImamuraTomohiro Sasamoto

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