Year: 2026
Type: preprint
Abstract: 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-dimensional lattice.
Source: arXiv (Cornell University)
Authors: Cai, Zhenhao, Ding, Jian
Institutions: Weizmann Institute of Science, Peking University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2306923292, G4301156662, G8700735110
OpenAlex ID: W7212014863