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Recently, Quastel and Remenik \cite{QRKP} [arXiv:1908.10353] found aremarkable relation between some solutions of the finite timeKardar-Parisi-Zhang (KPZ) equation and the Kadomtsev-Petviashvili (KP)equation. Using this relation we obtain the large deviations at large time andat short time for the KPZ equation with droplet initial conditions, and atshort time with half-Brownian initial conditions. It is consistent withprevious results and allows to obtain sub-leading corrections, as well asresults at intermediate time. In addition, we find that the appropriategenerating function associated to the full Brownian initial condition alsosatisfies the KP equation. Finally, generating functions for some linearstatistics of the Airy point process are also found to satisfy the KP property,and consequences are discussed.

Large deviations for the KPZ equation from the KP equation