3 papers
math.PR2025
Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs
Zhenhao Cai, Jian Ding
In this paper, we establish the existence and equivalence of four types of incipient infinite clusters (IICs) for the critical Gaussian free field (GFF) level-set and the critical…
math.PR2025
Quasi-multiplicativity and regularity for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
We prove quasi-multiplicativity for critical level-sets of Gaussian free fields (GFF) on the metric graphs (). Specifically, we study the probabi…
math.PR2024
Polynomial lower bound on the effective resistance for the one-dimensional critical long-range percolation
Jian Ding, Zherui Fan, Lu-Jing Huang
In this work, we study the critical long-range percolation on , where an edge connects and independently with probability for some fixe…