Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Tran, Tho, Nguyen, Tan M.
Institution: National University of Singapore
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212047102