论文标题
$κ= 8 $：UST和LERW在拓扑矩形中的收敛
Hypergeometric SLE with $κ=8$: Convergence of UST and LERW in Topological Rectangles
论文作者
论文摘要
我们认为在具有交替边界条件的拓扑矩形中，我们考虑了统一的跨越树（UST）。与UST相关的Peano曲线微弱地收敛到高几何SLE $ _8 $，由HSLE $ _8 $表示。从收敛结果中，我们获得了HSLE $ _8 $的连续性和可逆性，以及SLE $ _8 $和HSLE $ _8 $之间的有趣连接。 UST中的基于环的随机步行（LERW）分支微弱地收敛到SLE $ _2（-1，-1; -1; -1，-1）$。我们还获得了LERW分支两个端点的限制关节分布。
We consider uniform spanning tree (UST) in topological rectangles with alternating boundary conditions. The Peano curves associated to the UST converge weakly to hypergeometric SLE$_8$, denoted by hSLE$_8$. From the convergence result, we obtain the continuity and reversibility of hSLE$_8$ as well as an interesting connection between SLE$_8$ and hSLE$_8$. The loop-erased random walk (LERW) branch in the UST converges weakly to SLE$_2(-1, -1; -1, -1)$. We also obtain the limiting joint distribution of the two end points of the LERW branch.
