Percolation in majority dynamics

Abstract

We consider two-dimensional dependent dynamical site percolation where sites perform majority dynamics. We introduce the critical percolation function at time $t$ as the infimum density with which one needs to begin in order to obtain an infinite open component at time $t$. We prove that, for any fixed time $t$, there is no percolation at criticality and that the critical percolation function is continuous. We also prove that, for any positive time, the percolation threshold is strictly smaller than the critical probability for independent site percolation.