Abstract
We consider uniform spanning tree (UST) in topological polygons with marked points on the boundary with alternating boundary conditions. In an earlier work by Liu-Peltola-Wu, the authors derive the scaling limit of the Peano curve in the UST. They are variants of SLE. In this article, we derive the scaling limit of the loop-erased random walk branch (LERW) in the UST. They are variants of SLE. The conclusion is a generalization of an earlier work by Han-Liu-Wu where the authors derive the scaling limit of the LERW branch of UST when . When , the limiting law is SLE. However, the limiting law is no longer in the family of SLE process as long as .
Acknowledgments
H. W. is funded by Beijing Natural Science Foundation (JQ20001). We thank Eveliina Peltola for helpful discussion.
Citation
Mingchang Liu. Hao Wu. "Loop-erased random walk branch of uniform spanning tree in topological polygons." Bernoulli 29 (2) 1555 - 1577, May 2023. https://doi.org/10.3150/22-BEJ1510