Exponential decay of connection probabilities for subcritical Voronoi percolation in $$\mathbb {R}^d$$ R d

Abstract

We prove that for Voronoi percolation on $$\mathbb {R}^d$$ $$(d\ge 2)$$ , there exists $$p_c=p_c(d)\in (0,1)$$ such that For dimension 2, this result offers a new way of showing that $$p_c(2)=1/2$$ . This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition; see [10, 11].