论文标题
重量依赖性随机连接模型中的渗透相变
Percolation phase transition in weight-dependent random connection models
论文作者
论文摘要
我们研究了在$ d $维空间中定义的泊松过程点上定义的空间随机图，该空间结合了无标度分布和远程效果。每个泊松点都被分配一个独立的重量。考虑到点的重量和位置，我们独立地在任何对点之间形成边缘，具体取决于点的两个重量及其距离。优先于短边和与重量大的顶点的连接。我们表征存在非平凡渗透相变的参数制度，并表明它不仅取决于度分布的幂律指数，还取决于几何模型参数。我们将此结果应用于表征基于年龄的空间优先附着网络的鲁棒性。
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a nontrivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.
