标题： 动态环路方程 显示英文标题

标题： Dynamical Loop Equation

摘要： 我们引入了大型二维相互作用粒子系统家族的动力学版本的环（或Dyson-Schwinger）方程，包括Dyson布朗运动、非交叉伯努利/泊松随机游走、$\beta$-角过程、Gelfand-Tsetlin图式上的均匀和Jack变形测度、Macdonald过程以及在菱形镶嵌上的$(q,\kappa)$-分布。在技术假设下，我们证明动力学环方程导致高斯场类型的波动。作为应用，我们计算了菱形镶嵌上$(q,\kappa)$-分布的极限形状，并证明其高度波动在适当的复结构下收敛到高斯自由场。 显示英文摘要

摘要： 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, $\beta$--corners processes, uniform and Jack-deformed measures on Gelfand-Tsetlin patterns, Macdonald processes, and $(q,\kappa)$-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 $(q,\kappa)$--distributions on lozenge tilings and prove that their height fluctuations converge to the Gaussian Free Field in an appropriate complex structure.