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arXiv · 2608.27630

Oriented planar maps and annular mating of trees

Xingjian Di·Nina Holden·Zhenfeng Tu·Pu Yu
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Abstract

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 $\gamma=16\kappa^{-1/2}\in(0,2)$.

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Xingjian Di, Nina Holden, Zhenfeng Tu, Pu Yu. 2026-08-27. Oriented planar maps and annular mating of trees. https://arxiv.org/abs/2608.27630

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