标题： KPZ方程与Airy点过程之间的矩匹配 显示英文标题

标题： Moments Match between the KPZ Equation and the Airy Point Process

摘要： Amir-Corwin-Quastel、Calabrese-Le Doussal-Rosso、Dotsenko 以及 Sasamoto-Spohn 的结果表明，KPZ 方程在窄楔形初值条件下的解的一点分布与 Airy 确定性随机点过程的乘法统计分布一致。对两边取 Taylor 系数可得到矩恒等式。我们通过多变量积分表示的组合匹配，给出了这些恒等式的简单直接证明。 显示英文摘要

摘要： 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.