PreprintCC BY 4.0arXiv
Uniform meandric systems as percolation on planar maps: conjectures and a numerical study
Abstract
We perform a numerical study of uniform meandric systems via their encoding by pairs of simple random walks and their interpretation as a model of critical percolation on random planar maps. We investigate certain natural box-crossing events and provide numerical evidence for a strong negative association between opposite open crossings and formulate conjectures on their asymptotic behavior. Our second contribution is a simple law-preserving dynamics on meandric systems, by local peak/valley flips in the walk encoding. Our simulations suggest that the percolation structure decorrelates much faster than the underlying random planar map.
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BibTeX
@misc{wei2026uniform,
title = {{Uniform meandric systems as percolation on planar maps: conjectures and a numerical study}},
author = {David Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03730},
eprint = {2610.03730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03730},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniform meandric systems as percolation on planar maps: conjectures and a numerical study
AU - David Wei
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03730
UR - https://arxiv.org/abs/2610.03730
AB - We perform a numerical study of uniform meandric systems via their encoding by pairs of simple random walks and their interpretation as a model of critical percolation on random planar maps. We investigate certain natural box-crossing events and provide numerical evidence for a strong negative association between opposite open crossings and formulate conjectures on their asymptotic behavior. Our second contribution is a simple law-preserving dynamics on meandric systems, by local peak/valley flips in the walk encoding. Our simulations suggest that the percolation structure decorrelates much faster than the underlying random planar map.
ER -