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Percolation in majority dynamics. (English) Zbl 1439.82040

Summary: 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.

MSC:

82C43 Time-dependent percolation in statistical mechanics
82B43 Percolation
82C22 Interacting particle systems in time-dependent statistical mechanics
82C27 Dynamic critical phenomena in statistical mechanics
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