DYNAMICAL LOOP EQUATION

• 成果类型: Article
• 署名作者: Gorin, Vadim; Huang, Jiaoyang
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of Pennsylvania
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1685
• 发表日期: 2024
• 页码: 1758-1863
• 关键词: global fluctuations; local statistics; brownian-motion; general beta; UNIVERSALITY; asymptotics; geometry; tilings; wigner; eigenvalues

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.