One-arm probabilities for the two-dimensional metric-graph and discrete Gaussian free field
Probability
2026-03-27 v1
Abstract
We study the one-arm probability in the level-set percolation of the discrete and metric-graph Gaussian free field (GFF) defined on a box with Dirichlet boundary conditions. For the metric-graph case, we establish asymptotic estimates on two one-arm probabilities of interest. For the discrete case, we show up-to-constants bounds on the point-to-bulk probability and demonstrate its difference from the metric-graph case.
Keywords
Cite
@article{arxiv.2603.25400,
title = {One-arm probabilities for the two-dimensional metric-graph and discrete Gaussian free field},
author = {Yijie Bi and Yifan Gao and Xinyi Li},
journal= {arXiv preprint arXiv:2603.25400},
year = {2026}
}
Comments
24 pages