论文标题
二聚体模型和全态函数在平面图的T件上
Dimer model and holomorphic functions on t-embeddings of planar graphs
论文作者
论文摘要
我们介绍了在加权双分部分平面图的T插入上的离散全态函数的框架； T-安排在最近的论文Arxiv：1810.05616中也以库仑的名称出现。我们认为，该框架与相应二聚体模型中高度波动的缩放限制的分析特别相关。特别是，它统一了Kenyon对二聚体可观察物的解释是T-Graphs上谐波函数的衍生物，以及Smirnov在关键ISING模型上的工作中的S旋晶函数概念。我们为此类功能开发了先验的规律性理论，并提供了有关高度波动向高斯自由场的收敛性的元理论。我们还讨论了复杂分析的几种更高的标准离散化如何符合此一般框架。
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent paper arXiv:1810.05616. We argue that this framework is particularly relevant for the analysis of scaling limits of the height fluctuations in the corresponding dimer models. In particular, it unifies both Kenyon's interpretation of dimer observables as derivatives of harmonic functions on T-graphs and the notion of s-holomorphic functions originated in Smirnov's work on the critical Ising model. We develop an a priori regularity theory for such functions and provide a meta-theorem on convergence of the height fluctuations to the Gaussian Free Field. We also discuss how several more standard discretizations of complex analysis fit this general framework.
