No infinite clusters at criticality for two-dimensional dependent percolation under abstract hypotheses
arXiv:2607.13308
The paper provides a general set of conditions that guarantee no infinite clusters appear at the critical point for a wide range of two‑dimensional dependent percolation models, and shows how these conditions recover known results for models like Gaussian level‑set and Boolean percolation.
Abstract
We establish a general criterion ensuring the absence of infinite connected components at criticality for a broad class of two-dimensional dependent percolation models. Our assumptions include monotonicity, stationarity and ergodicity, positive association, a quantitative decoupling condition, continuity in the percolation parameter, and trivial behavior at the extremes. As application, we show how our criterion recovers known results for classical dependent percolation models, such as Gaussian level-set percolation and Boolean percolation.
17 pages