论文标题
关键不均匀随机图中最大组件的上限
Upper bounds for the largest components in critical inhomogeneous random graphs
论文作者
论文摘要
我们考虑Norros-Reittu随机图$ nr_n（\ textbf {w}）$，其中边缘是独立存在的，但是边缘概率通过顶点权重进行了调节，并在关键时使用基于martingales的概率参数来分析此模型中的组件大小。特别是，我们获得了更强的上限（相对于文献中的那些），以观察到异常大的最大簇，并简化得出多项式上限所需的参数，以观察到异常最大的组件。
We consider the Norros-Reittu random graph $NR_n(\textbf{w})$, where edges are present independently but edge probabilities are moderated by vertex weights, and use probabilistic arguments based on martingales to analyse the component sizes in this model when considered at criticality. In particular, we obtain stronger upper bounds (with respect to those available in the literature) for the probability of observing unusually large maximal clusters, and simplify the arguments needed to derive polynomial upper bounds for the probability of observing unusually small largest components.
