论文标题
Riemann表面上的二聚体II：保形不变性和缩放极限
Dimers on Riemann surfaces II: conformal invariance and scaling limit
论文作者
论文摘要
鉴于有限的拓扑类型有界有限的$ m $，我们显示了在任何合理意义上大约$ m $的图表上的跨循环跨越森林的通用和共同不变的缩放限制（本质上，不变性原则上都有，并且步行是满足交叉假设的）。结合伴侣纸ARXIV：1908.00832，这证明了此类图中的temperleyan二聚体模型的高度函数的通用，不变的缩放限制的存在。在此过程中，我们描述了termleyan CRSF和循环措施之间的关系，并开发独立感兴趣的工具，仅在随机步行中进行粗暴控制，以研究后者
Given a bounded Riemann surface $M$ of finite topological type, we show the existence of a universal and conformally invariant scaling limit for the Temperleyan cycle-rooted spanning forest on any sequence of graphs which approximate $M$ in a reasonable sense (essentially, the invariance principle holds and the walks satisfy a crossing assumption). In combination with the companion paper arxiv:1908.00832, this proves the existence of a universal, conformally invariant scaling limit for the height function of the Temperleyan dimer model on such graphs. Along the way, we describe the relationship between Temperleyan CRSFs and loop measures, and develop tools of independent interest to study the latter using only rough control on the random walk
