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Article Dans Une Revue EPL - Europhysics Letters Année : 2022

Steady state of the KPZ equation on an interval and Liouville quantum mechanics

Résumé

We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval $[0,L]$ 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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Dates et versions

hal-03357596 , version 1 (28-09-2021)

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Pierre Le Doussal, Guillaume Barraquand. Steady state of the KPZ equation on an interval and Liouville quantum mechanics. EPL - Europhysics Letters, 2022, ⟨10.1209/0295-5075/ac25a9⟩. ⟨hal-03357596⟩
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