Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wei, David
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220674647