论文标题
平面渗透的跨越概率
Crossing probabilities for planar percolation
论文作者
论文摘要
我们证明，对于满足正相关的任何不变的平面渗透过程，一般的Russo-Seymour-Welsh结果有效。这意味着，沿较长方向跨矩形的概率是通过同态形态与沿短方向交叉的概率有关的。这种同质形态是普遍的，因为它仅取决于矩形的纵横比，并且在规模和考虑的模型上是统一的。
We prove a general Russo-Seymour-Welsh result valid for any invariant planar percolation process satisfying positive association. This means that the probability of crossing a rectangle in the long direction is related by a homeomorphism to the probability of crossing it in the short direction. This homeomorphism is universal in the sense that it depends only on the aspect ratio of the rectangle, and is uniform in the scale and the considered model.
