Crossing probabilities for Voronoi percolation. (English) Zbl 1352.60130

Tassion, Vincent

Ann. Probab. 44, No. 5, 3385-3398 (2016).

Summary: We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, such as the polynomial decay of the one-arm event at criticality.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B43	Percolation
82B21	Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics

Keywords:

Voronoi percolation; crossing probabilities; Russo-Seymour-Welsh theory; box-crossing property