平面LERW和UST中的边界相关性
Boundary correlations in planar LERW and UST
摘要：
我们发现明确的公式一般边界访问事件的概率平面环擦除随机游动，以及连接事件的分支在统一的生成树。我们表明，这两种概率，适当重整化时，收敛在标度限制共形协变函数，满足偏微分方程的二阶和三阶，预测的共形场论。缩放极限连通性概率还提供了在$κ=2$处的多个$\mathrm{SLE}_κ$的纯配分函数的公式。
英文摘要：
We find explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks, as well as connectivity events for branches in the uniform spanning tree. We show that both probabilities, when suitably renormalized, converge in the scaling limit to conformally covariant functions which satisfy partial differential equations of second and third order, as predicted by conformal field theory. The scaling limit connectivity probabilities also provide formulas for the pure partition functions of multiple $\mathrm{SLE}_κ$ at $κ=2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
