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arXiv · 2609.07026

Locality of Bernoulli Site Percolation on Transitive Graphs

Tho Tran·Tan M. Nguyen
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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.

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Tho Tran, Tan M. Nguyen. 2026-09-07. Locality of Bernoulli Site Percolation on Transitive Graphs. https://arxiv.org/abs/2609.07026

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