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Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters
Abstract
We consider the level sets of the Gaussian free field and the vacant set of random interlacements, both defined on a typical realization of the infinite cluster of supercritical Bernoulli bond percolation on ℤd, d ≥ 3. We prove that in the entire supercritical regime of Bernoulli bond percolation, both the level sets of the Gaussian free field and the vacant set of random interlacements undergo non-trivial percolation phase transitions at deterministic critical levels. A key aspect of the proof is the development of certain quenched controls over tree embeddings, permitting the application of a static renormalization scheme in the presence of spatial irregularities, which may be of independent interest.
Related
- Non-perturbative finite connectivities in supercritical Bernoulli percolation on ℤd with d≥ 3
- Continuity of the phase transition for long-range Bernoulli percolation with exponential decay on ℤ2
- Locality of Bernoulli Site Percolation on Transitive Graphs
- Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices
- Distribution tail of the distance to infinity in supercritical bond percolation
BibTeX
@misc{chiarini2026phase,
title = {{Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters}},
author = {Alberto Chiarini and Zhizhou Liu and Maximilian Nitzschner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08882},
eprint = {2609.08882},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08882},
}
RIS
TY - UNPB
TI - Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters
AU - Alberto Chiarini
AU - Zhizhou Liu
AU - Maximilian Nitzschner
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08882
UR - https://arxiv.org/abs/2609.08882
AB - We consider the level sets of the Gaussian free field and the vacant set of random interlacements, both defined on a typical realization of the infinite cluster of supercritical Bernoulli bond percolation on ℤ^d, d ≥ 3. We prove that in the entire supercritical regime of Bernoulli bond percolation, both the level sets of the Gaussian free field and the vacant set of random interlacements undergo non-trivial percolation phase transitions at deterministic critical levels. A key aspect of the proof is the development of certain quenched controls over tree embeddings, permitting the application of a static renormalization scheme in the presence of spatial irregularities, which may be of independent interest.
ER -