Speaker: 蔡振豪博士，Weizmann Institute of Science

Inviter: 石权副研究员

Title: Incipient Infinite Clusters in Metric Graph Gaussian Free Fields

Language: Chinese

Time & Venue: 2025.01.16 10:45-10:45 南楼N613

Abstract: The Gaussian free field (GFF) on the metric graph was introduced by Titus Lupu (2016) as a natural extension of the discrete GFF. Its level-set (i.e., the collection of points where the GFF exceeds a given threshold) is a random object with favorable properties and a strong connection to numerous models in statistical physics (including loop soups, random interlacements, etc). This talk will introduce our recent progress in establishing the incipient infinite clusters of this level-set, as well as a series of regularity properties for its connecting probabilities. Some of these properties lead to new conjectures in Bernoulli percolation. This is a joint work with Jian Ding (Peking University).