论文标题
UST分支，Martingales和多个SLE（2）
UST branches, martingales, and multiple SLE(2)
论文作者
论文摘要
我们将统一跨越树（UST）中多个边界至结合分支的局部缩放限制为局部多重SLE（2），即通过合适的分区函数加权加权的SLE（2）过程。通过最近的结果，这也表征了完整曲线的完整集合的“全局”缩放限制。该标识是基于UST中可观察到的$ N $分支机构的Martingale，通过通过模型的离散分区功能将UST的众所周知的Martingale加权来获得。离散的martingales和限制SLE过程的加权转换仅依赖于离散的域Markov属性和（基本上）分区函数的收敛性。我们通过为边界访问的UST分支和边界访问的SLE绘制类似的收敛证明来说明它们的推广性（2）。
We identify the local scaling limit of multiple boundary-to-boundary branches in a uniform spanning tree (UST) as a local multiple SLE(2), i.e., an SLE(2) process weighted by a suitable partition function. By recent results, this also characterizes the "global" scaling limit of the full collection of full curves. The identification is based on a martingale observable in the UST with $N$ branches, obtained by weighting the well-known martingale in the UST with one branch by the discrete partition functions of the models. The obtained weighting transforms of the discrete martingales and the limiting SLE processes, respectively, only rely on a discrete domain Markov property and (essentially) the convergence of partition functions. We illustrate their generalizability by sketching an analogous convergence proof for a boundary-visiting UST branch and a boundary-visiting SLE(2).
