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

Zhenhao Cai; Jian Ding

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arXiv · 2609.08702

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

Zhenhao Cai·Jian Ding

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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.

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Zhenhao Cai, Jian Ding. 2026-09-08. Scaling Limit of Critical Loop Soup Clusters in Three, Four, and Five Dimensions. https://arxiv.org/abs/2609.08702

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