Moments Match between the KPZ Equation and the Airy Point Process

Alexei Borodin ab and Vadim Gorin ab
a) Department of Mathematics, Massachusetts Institute of Technology, USA
b) Institute for Information Transmission Problems of Russian Academy of Sciences, Russia

Received August 09, 2016, in final form October 21, 2016; Published online October 26, 2016

Abstract
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.

Key words: KPZ equation; Airy point process.

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