Pierre Le Doussal
Published 2019-10-08Version 1
Recently, Quastel and Remenik \cite{QRKP} [arXiv:1908.10353] found a remarkable relation between some solutions of the finite time Kardar-Parisi-Zhang (KPZ) equation and the Kadomtsev-Petviashvili (KP) equation. Using this relation we obtain the large deviations at large time and at short time for the KPZ equation with droplet initial conditions, and at short time with half-Brownian initial conditions. It is consistent with previous results and allows to go beyond. In addition, we find that the appropriate generating function associated to the full Brownian initial condition also satisfies the KP equation. Extensions to generating functions for linear statistics of the Airy point process, which are found to also satisfy the KP property, are briefly discussed.
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