亚临界 Norros-Reittu 模型中的大分量
Large components in the subcritical Norros-Reittu model
AI总结：
本文研究亚临界 Norros-Reittu 随机图中各分量的顶点计数，证明其点过程收敛于泊松过程，并由此得到最大分量规模及最大叶子数的渐近结果，结果也适用于 Chung-Lu 模型和广义随机图。
摘要：
Norros-Reittu 模型是一个具有 $n$ 个顶点且被赋予独立同分布权重的随机图。任意两个顶点之间的边数服从独立的泊松分布，其参数随这两个顶点的权重增大而增大。选择合适的权重分布可导致度分布呈现幂律行为，正如在许多现实世界复杂网络中所观察到的那样。我们在亚临界区域研究该模型，即不存在巨分量的情形。对于每个分量，我们统计其顶点数，并证明相应的点过程收敛于一个泊松过程。更一般地，也可以只统计每个分量中的特定顶点，例如叶子。由此可以推导出关于最大分量的大小或单个分量中叶子最大数量的渐近结果。这些结果同样适用于 Chung-Lu 模型和广义随机图。
英文摘要：
The Norros-Reittu model is a random graph with $n$ vertices and i.i.d. weights assigned to them. The number of edges between any two vertices follows an independent Poisson distribution whose parameter is increasing in the weights of the two vertices. Choosing a suitable weight distribution leads to a power-law behaviour of the degree distribution as observed in many real-world complex networks. We study this model in the subcritical regime, i.e. in the absence of a giant component. For each component, we count the vertices and show convergence of the corresponding point process to a Poisson process. More generally, one can also count only specific vertices per component, like leaves. From this one can deduce asymptotic results on the size of the largest component or the maximal number of leaves in a single component. The results also apply to the Chung-Lu model and the generalised random graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
