Geometry of the random interlacement
Geometry of the random interlacement
复制标题
随机交错的几何形状
DOI：
10.1214/ecp.v16-1660
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发表时间：
2011
影响因子：
0.5
通讯作者：
Johan Tykesson
中科院分区：
文献类型：
--
作者：
Eviatar B. Procaccia;Johan Tykesson
我们考虑了d维晶格上随机交错的几何。我们使用[1]中发展的随机维理论的思想来证明以下内容：给定两个顶点$x,y$属于交错集，则有可能找到$x$和$y$之间的路径，该路径包含在来自潜在泊松点过程的至多$ $ lceil d/2 $ rceil$轨迹所留下的轨迹中。此外，这个结果在某种意义上是尖锐的，即在置换集中有对点不能通过使用最多$ $ rceil1 /2 $轨迹的轨迹来连接。
We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory developed in [1] to prove the following: Given that two vertices $x,y$ belong to the interlacement set, it is possible to find a path between $x$ and $y$ contained in the trace left by at most $\lceil d/2 \rceil$ trajectories from the underlying Poisson point process. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most $\lceil d/2 \rceil-1$ trajectories.