Percolation for level-sets of Gaussian free fields on metric graphs
Probability
2019-03-14 v2
Abstract
We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity and the bound is sharp up to a poly-logarithmic factor with an exponent of one-quarter. This substantially improves a previous result by Li and the first author. In three dimensions and higher, we provide rather sharp estimates of percolation probabilities in different regimes which altogether describe a sharp phase transition.
Keywords
Cite
@article{arxiv.1807.11117,
title = {Percolation for level-sets of Gaussian free fields on metric graphs},
author = {Jian Ding and Mateo Wirth},
journal= {arXiv preprint arXiv:1807.11117},
year = {2019}
}
Comments
29 pages; removed Proposition 12 from Section 2, revised argument in Section 3, 4.1, and 4.3. Results unchanged