| Issue |
EPL
Volume 137, Number 6, March 2022
|
|
|---|---|---|
| Article Number | 61003 | |
| Number of page(s) | 7 | |
| Section | Statistical physics and networks | |
| DOI | https://doi.org/10.1209/0295-5075/ac25a9 | |
| Published online | 06 May 2022 | |
Steady state of the KPZ equation on an interval and Liouville quantum mechanics
Laboratoire de Physique de l'École Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université de Paris - 24 rue Lhomond, 75231 Paris, France
(a) guillaume.barraquand@ens.fr (corresponding author)
Received: 17 June 2021
Accepted: 10 September 2021
We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval ![$[0,L]$](/articles/epl/abs/2022/06/epl21100337/epl21100337_tex_eq1.png)
with general Neumann-type boundary conditions and any interval size. This is achieved using the recent results of Corwin and Knizel (arXiv:2103.12253) together with Liouville quantum mechanics. Our formula allows to easily determine the stationary measure in various limits: KPZ fixed point on an interval, half-line KPZ equation, KPZ fixed point on a half-line, as well as the Edwards-Wilkinson equation on an interval.
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