论文标题
泊松人不均匀的随机多编码的连通性
Connectivity of Poissonian Inhomogeneous random Multigraphs
论文作者
论文摘要
我们引入了一种新的方法，用于采样不均匀的随机图，旨在在学位序列和单个边缘概率的分配中具有很大的灵活性，同时保持可拖动。为此，我们在平方$ [0,1]^2 $上运行泊松点过程，其强度与内核$ W（x，y）$成比例，并识别图形的每个顶点，并带有正方形的子集，如果在此子集中有一个点，则在它们之间增加边缘。这样可以确保边缘之间的无条件独立性，并使在这种情况下比其他类似模型更容易证明许多陈述。在这里，我们在$ W（x，y）$上的轻度集成性条件下证明了连通性阈值的清晰度。
We introduce a new way to sample inhomogeneous random graphs designed to have a lot of flexibility in the assignment of the degree sequence and the individual edge probabilities while remaining tractable. To achieve this we run a Poisson point process over the square $[0,1]^2$, with an intensity proportional to a kernel $W(x,y)$ and identify every couple of vertices of the graph with a subset of the square, adding an edge between them if there is a point in such subset. This ensures unconditional independence among edges and makes many statements much easier to prove in this setting than in other similar models. Here we prove sharpness of the connectivity threshold under mild integrability conditions on $W(x,y)$.
