论文标题
基于固定点过程的图表中没有渗透，其程度由两个界定
Absence of percolation in graphs based on stationary point processes with degrees bounded by two
论文作者
论文摘要
我们将出现的无向图视为固定点过程的确定性函数，使每个点的度数都受两个界限。对于大量的点过程和边缘绘制规则，我们显示出的图几乎没有无限连接的组件。特别是，这扩展了基于稳定的Cox点过程的SINR图的先前结果，并验证了Balister和Bollobás的猜想，即双向$ k $ k $ - near的二维同质poisson点过程的最邻居图不会渗透$ k = 2 $。
We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for SINR graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional $k$-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for $k=2$.
