论文标题
优先附件模型的当地限制的通用性
Universality of the local limit of preferential attachment models
论文作者
论文摘要
我们研究了优先依恋模型，其中顶点进入I.I.D.网络。我们称之为外观的随机数。我们确定了此类模型的局部限制，大大扩展了Berger等人（2014年）的工作。我们称之为随机的pólya点树的限制随机图的程度分布具有令人惊讶的大小偏见现象。许多现有的优先附件模型可以看作是我们与I.I.D.的优先附件模型的特殊情况。超级。此外，我们的模型包含了优先附件适应性参数的负值，这使我们可以考虑具有无限差异度的优先依恋模型。我们的本地融合证明包括两个主要步骤：Pólyaurn的图表描述，以及对其中的社区的明确识别。我们提供了一个新颖而明确的证据，以在优先附着模型和Pólyaurn图之间建立耦合。我们的结果证明了固定年龄在局部极限的顶点的密度收敛结果。
We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014). The degree distribution of this limiting random graph, which we call the random Pólya point tree, has a surprising size-biasing phenomenon. Many of the existing preferential attachment models can be viewed as special cases of our preferential attachment model with i.i.d. out-degrees. Additionally, our models incorporate negative values of the preferential attachment fitness parameter, which allows us to consider preferential attachment models with infinite-variance degrees. Our proof of local convergence consists of two main steps: a Pólya urn description of our graphs, and an explicit identification of the neighbourhoods in them. We provide a novel and explicit proof to establish a coupling between the preferential attachment model and the Pólya urn graph. Our result proves a density convergence result, for fixed ages of vertices in the local limit.
