Author

Zhen-Hao Cai

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Open access Oct 2026

Quasi-multiplicativity and Regularity for Metric Graph Gaussian Free Fields

We prove quasi-multiplicativity for critical level-sets of Gaussian free fields (GFF) on the metric graphs Z~d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt...

Jian Ding, Zhen-Hao Cai · Communications in Mathematic... · 0 citations

Preprint Sep 2026

Scaling Limit of Critical Loop Soup Clusters in Three, Four, and Five Dimensions

We prove that on the metric graph of $\mathbb{Z}^d$ for $d\in \{3,4,5\}$, clusters of the critical loop soup (or equivalently, clusters of the critical Gaussian free field level-set) admit a scaling limit. To the best of our knowledge, this presents the first scaling limit result for a percolation model on a three-dime...

Zhen-Hao Cai, Jian Ding · 0 citations