  The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, and
Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ
equation with the narrow wedge initial condition coincides with that for a
multiplicative statistics of the Airy determinantal random point process.
Taking Taylor coefficients of the two sides yields moment identities. We
provide a simple direct proof of those via a combinatorial match of their
multivariate integral representations.
