Moments Match between the KPZ Equation and the Airy Point Process
Mathematical Physics
2016-10-27 v2 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1608.01557,
title = {Moments Match between the KPZ Equation and the Airy Point Process},
author = {Alexei Borodin and Vadim Gorin},
journal= {arXiv preprint arXiv:1608.01557},
year = {2016}
}