PreprintCC BY 4.0arXiv
Locality of Bernoulli Site Percolation on Transitive Graphs
Abstract
We prove locality of the critical probability for Bernoulli site percolation on infinite, connected, locally finite, vertex-transitive graphs, under the usual assumption that the critical probabilities stay uniformly below one. The proof develops site-percolation forms of the two-ghost inequality, sharp-threshold and snowballing estimates, and the nonunimodular height method. We also establish the plentiful-tube geometry needed for the multiscale argument from quantitative structure and random-walk estimates.
Related
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- Non-perturbative finite connectivities in supercritical Bernoulli percolation on ℤd with d≥ 3
BibTeX
@misc{tran2026locality,
title = {{Locality of Bernoulli Site Percolation on Transitive Graphs}},
author = {Tho Tran and Tan M. Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07026},
eprint = {2609.07026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07026},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Locality of Bernoulli Site Percolation on Transitive Graphs
AU - Tho Tran
AU - Tan M. Nguyen
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07026
UR - https://arxiv.org/abs/2609.07026
AB - We prove locality of the critical probability for Bernoulli site percolation on infinite, connected, locally finite, vertex-transitive graphs, under the usual assumption that the critical probabilities stay uniformly below one. The proof develops site-percolation forms of the two-ghost inequality, sharp-threshold and snowballing estimates, and the nonunimodular height method. We also establish the plentiful-tube geometry needed for the multiscale argument from quantitative structure and random-walk estimates.
ER -