Title: Percolation in Metric Graph Gaussian Free Fields
Abstract: The Gaussian free field (GFF) on the metric graph, introduced by Titus
Lupu (2016), is 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 strong connections to numerous models in statistical
physics (including loop soups, random interlacements, etc). This talk will introduce
our recent progress in establishing its critical one-arm exponents, volume exponents,
quasi-multiplicativity and incipient infinite clusters. Some of these results lead to new
conjectures in Bernoulli percolation. This is a joint work with Jian Ding (Peking
University).