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PreprintCC BY-SA 4.0arXiv

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 γ=16κ−1/2∈(0,2).

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Cite

BibTeXRIS
BibTeX
@misc{di2026oriented,
  title = {{Oriented planar maps and annular mating of trees}},
  author = {Xingjian Di and Nina Holden and Zhenfeng Tu and Pu Yu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27630},
  eprint = {2608.27630},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27630},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Oriented planar maps and annular mating of trees
AU  - Xingjian Di
AU  - Nina Holden
AU  - Zhenfeng Tu
AU  - Pu Yu
PY  - 2026
DA  - 2026/08/27
PB  - arXiv
DO  - 10.48550/arxiv.2608.27630
UR  - https://arxiv.org/abs/2608.27630
AB  - 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∈(0,2).
ER  -