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The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, andSasamoto-Spohn imply that the one-point distribution of the solution of the KPZequation with the narrow wedge initial condition coincides with that for amultiplicative statistics of the Airy determinantal random point process.Taking Taylor coefficients of the two sides yields moment identities. Weprovide a simple direct proof of those via a combinatorial match of theirmultivariate integral representations.

Moments Match between the KPZ Equation and the Airy Point Process