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Scaling Limit of Critical Loop Soup Clusters in Three, Four, and Five Dimensions
Abstract
We prove that on the metric graph of ℤd for d∈ {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.
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BibTeX
@misc{cai2026scaling,
title = {{Scaling Limit of Critical Loop Soup Clusters in Three, Four, and Five Dimensions}},
author = {Zhenhao Cai and Jian Ding},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08702},
eprint = {2609.08702},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08702},
}
RIS
TY - UNPB
TI - Scaling Limit of Critical Loop Soup Clusters in Three, Four, and Five Dimensions
AU - Zhenhao Cai
AU - Jian Ding
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08702
UR - https://arxiv.org/abs/2609.08702
AB - We prove that on the metric graph of ℤ^d for d∈ {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.
ER -