论文标题
无尺度几何随机图上的接触过程
The contact process on scale-free geometric random graphs
论文作者
论文摘要
我们研究了具有无尺度分布的一类几何随机图上的接触过程，该图在$ \ mathbb {r}^d $上的泊松点过程中定义。该类包括与年龄有关的随机连接模型和软布尔模型。在这些随机图的超质状态中，当感染率较小并显示这些图的有限版本时，我们提供了非迫使概率的精确渐近，即灭绝时间在图形的大小中是指数级的。
We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph.
