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arXiv · 1608.01557

Moments Match between the KPZ Equation and the Airy Point Process

Alexei Borodin·Vadim Gorin
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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.

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Alexei Borodin, Vadim Gorin. 2016-08-04. Moments Match between the KPZ Equation and the Airy Point Process. https://doi.org/10.3842/sigma.2016.102

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