Moments Match between the KPZ Equation and the Airy Point Process
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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 equa-tion 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.
Date issued
2016-09Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Symmetry, Integrability and Geometry: Methods and Applications
Publisher
Raboud University
Citation
Borodin, Alexei, and Vadim Gorin. “Moments Match Between the KPZ Equation and the Airy Point Process.” Symmetry, Integrability and Geometry: Methods and Applications 12, 102 (October 2016) © 2016 Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Raboud University
Version: Final published version
ISSN
1815-0659