通过最外边界III渗流的对偶性：Plus连通分量
Duality in percolation via outermost boundaries III: Plus connected components
摘要：
以$S_0$为原点，将$\mathbb{R}^2$平铺成不相交的单位正方形$\{S_k\}_{k \geq 0}$，如果$S_i$和$S_j$共享一个角，则它们是星形相邻的，如果它们共享一条边，则它们是加号相邻的。每一个广场不是空着就是有人。在本文中，我们使用Ganesan（2017）中导出的最外边界的结构，在以下意义上交替地获得星连通分量和正连通分量之间的对偶性：有一个空正方形的星连通环连接到并包围包含原点的有限正连通分量。
英文摘要：
Tile $\mathbb{R}^2$ into disjoint unit squares $\{S_k\}_{k \geq 0}$ with the origin being the centre of $S_0$ and say that $S_i$ and $S_j$ are star adjacent if they share a corner and plus adjacent if they share an edge. Every square is either vacant or occupied. In this paper, we use the structure of the outermost boundaries derived in Ganesan (2017) to alternately obtain duality between star and plus connected components in the following sense: There is a star connected cycle of vacant squares attached to and surrounding the finite plus connected component containing the origin.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
