PERCOLATION FOR LEVEL-SETS OF GAUSSIAN FREE FIELDS ON METRIC GRAPHS

• 成果类型: Article
• 署名作者: Ding, Jian; Wirth, Mateo
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1397
• 发表日期: 2020
• 页码: 1411-1435
• 关键词: random interlacements; clusters

摘要

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 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 precise estimates of percolation probabilities in different regimes which altogether describe a sharp phase transition.