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Percolation in majority dynamics

机译:多数动态的渗透

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摘要

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.
机译:我们考虑网站执行多数动态的二维依赖动态站点渗透。我们在时间$ T $介绍临界渗透功能,因为需要开始的最小密度,以便在$ $ $获得无限的开放组件。我们证明,对于任何固定的时间$ t $,没有临界不受渗透,并且临界渗透功能是连续的。我们还证明,对于任何阳性时间,渗透阈值严格小于独立部位渗透的关键概率。

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