AI 中文总结
该研究探讨与双极定向地图相关的定向环形平面地图，通过二维格点游走编码并结合树配对结果，揭示其与布朗路径、LQG环形及空间填充SLE环的关联。
AI 中文摘要
我们研究一类与双极定向地图密切相关的定向环形平面地图，证明此类地图可由二维格点游走编码，其在尺度极限下收敛于二维布朗路径。进一步证明环形的树配对结果：上述布朗路径及其推广形式可编码由参数为γ=16κ⁻¹/²∈(0,2)的逆时针空间填充SLE环装饰的LQG环形。
英文摘要
We study a class of oriented annular planar maps which are closely related to bipolar-oriented maps. We prove that such maps can be encoded by a 2D lattice walk which converges to a 2D Brownian path in the scaling limit. We further prove a mating-of-trees result for the annulus, where the aforementioned Brownian path and a generalization encodes an LQG annulus decorated by a counterclockwise space-filling SLE loop with parameter $γ=16κ^{-1/2}\in(0,2)$.
Comments56 pages, 24 figures
