论文标题
通过差分不平等的渗透噪声敏感性
Noise sensitivity of percolation via differential inequalities
论文作者
论文摘要
考虑临界伯努利在飞机上的渗透。我们给出了新的证明Garban，Pete和Schramm所示的尖锐噪音敏感性定理。与以前的方法相反，我们不使用任何光谱工具。我们宁愿根据凯斯滕（Kesten）的扩展关系证明，通过动态的四臂事件满足了不同的不平等现象。我们还获得了动态渗透的新结果。特别是，我们证明了原始和双重渗透的一组时间的豪斯多夫尺寸等于$ 2/3 $ a.s.
Consider critical Bernoulli percolation in the plane. We give a new proof of the sharp noise sensitivity theorem shown by Garban, Pete and Schramm. Contrary to the previous approaches, we do not use any spectral tool. We rather study differential inequalities satisfied by a dynamical four-arm event, in the spirit of Kesten's proof of scaling relations. We also obtain new results in dynamical percolation. In particular, we prove that the Hausdorff dimension of the set of times with both primal and dual percolation equals $2/3$ a.s.
