非齐次随机图的对偶性及割度量
Duality in inhomogeneous random graphs, and the cut metric
摘要：
经典的随机图模型$G(n,λ/n)$满足一个“对偶原理”，即从模型的超临界实例中去除巨组件会留下（基本上）一个亚临界实例。这些原则已被证明为各种模型;他们是有用的，因为它往往是更容易研究亚临界模型比直接研究超临界模型中的小组件。在这里，我们证明了这种类型的一个非常一般的一类随机图的边缘之间的独立性，定义的边缘概率矩阵的收敛性在切割度量的对偶原则。
英文摘要：
The classical random graph model $G(n,λ/n)$ satisfies a `duality principle', in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved for various models; they are useful since it is often much easier to study the subcritical model than to directly study small components in the supercritical model. Here we prove a duality principle of this type for a very general class of random graphs with independence between the edges, defined by convergence of the matrices of edge probabilities in the cut metric.
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