Speaker: 蔡振豪博士，Weizmann Institute of Science

Inviter: 石权副研究员

Title: One-arm Probabilities for Metric Graph Gaussian Free Fields below and at the Critical Dimension

Language: Chinese

Time & Venue: 2025.01.16 10:00-10:40 南楼N613

Abstract: The Gaussian free field (GFF) on metric graphs was introduced by Titus Lupu (2016) as a natural extension of the discrete GFF. Since then, due to its favorable properties and close connection to other statistical physics models, it has been extensively studied for years, especially in estimating the one-arm probability (i.e., the probability that the origin is connected to the boundary of the box centered at the origin with side length N by some connected set where GFF values are all positive). In recent works, we derive the exact orders of one-arm probabilities for all dimensions except the critical dimension d=6. This talk will present the proof idea for low-dimensional cases (d=3,4,5,6), which relies on a proof by contradiction and employs a coarse-graining argument at a fictitious scale. Notably, the critical dimension d=6 emerges naturally and unexpectedly from this framework. This is a joint work with Jian Ding (Peking University).