论文标题
动力循环方程
Dynamical Loop Equation
论文作者
论文摘要
我们为二维相互作用的粒子系统的大型循环（或Dyson-Schwinger）方程式引入动力版本，包括Dyson Brownian Motion，非降低Bernoulli/Poisson随机步行，$β$ - 角落流程 - 拐角，均匀的和千斤顶的型号和千斤顶的麦克斯林图案，MacDonald Processes，$（$）$（$），$（Q. q. Q. Q.瓷砖。在技术假设下，我们表明动态循环方程会导致高斯场类型波动。 作为应用程序，我们计算了$（Q，κ）$的极限形状 - lozenge tilings上的分布，并证明它们的高度波动在适当的复杂结构中融合到高斯自由场。
We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, $β$--corners processes, uniform and Jack-deformed measures on Gelfand-Tsetlin patterns, Macdonald processes, and $(q,κ)$-distributions on lozenge tilings. Under technical assumptions, we show that the dynamical loop equations lead to Gaussian field type fluctuations. As an application, we compute the limit shape for $(q,κ)$--distributions on lozenge tilings and prove that their height fluctuations converge to the Gaussian Free Field in an appropriate complex structure.
