Hypergeometric SLE with $\kappa=8$: Convergence of UST and LERW in Topological Rectangles

Yong Han; Mingchang Liu; Hao Wu

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arXiv · 2008.00403

Hypergeometric SLE with $\kappa=8$: Convergence of UST and LERW in Topological Rectangles

Yong Han·Mingchang Liu·Hao Wu

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Abstract

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.

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BibTeX RIS

Yong Han, Mingchang Liu, Hao Wu. 2020-08-02. Hypergeometric SLE with $\kappa=8$: Convergence of UST and LERW in Topological Rectangles. https://arxiv.org/abs/2008.00403

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