论文标题
无限渗透簇中图距离的差异为sublerear
The variance of the graph distance in the infinite cluster of percolation is sublinear
论文作者
论文摘要
我们考虑I.I.D.的标准模型$ \ Mathbb z^D $参数$ p $的债券渗透。当$ p> p_c $时，几乎肯定存在一个独特的无限群集$ \ Mathcal C_P $。使用CERF和Dembin的最新技术，我们证明了$ \ Mathcal C_P $在$ \ Mathcal C_P $之间的图形距离的差异是Sublinear。主要结果扩展了本杰米尼，卡莱和施拉姆，贝纳米和罗西诺和达姆，汉森和索斯的作品，以研究第一次通过渗透中的通行时间方差，而没有瞬间条件在边缘重量分布上。
We consider the standard model of i.i.d. bond percolation on $\mathbb Z^d$ of parameter $p$. When $p>p_c$, there exists almost surely a unique infinite cluster $\mathcal C_p$. Using the recent techniques of Cerf and Dembin, we prove that the variance of the graph distance in $\mathcal C_p$ between two points of $\mathcal C_p$ is sublinear. The main result extends the works of Benjamini, Kalai and Schramm, Benaim and Rossignol and Damron, Hanson and Sosoe for the study of the variance of passage times in first passage percolation without moment conditions on the edge-weight distribution.
