论文标题
重型制度中关键配置模型的全球较低质量结合
Global lower mass-bound for critical configuration models in the heavy-tailed regime
论文作者
论文摘要
当学位分布具有无限的第三刻时，我们为配置模型的临界窗口中最大的连接组件建立了全局较低的质量结合属性。相对于Gromov-Weak拓扑，在[7]中建立了临界渗滤簇的缩放限制，被视为测量的度量空间。我们的结果将这些缩放限制的结果扩展到了对学位分布的假设稍强的较强的Gromov-Hausdorff-Prokhorov拓扑。这意味着全局功能的分布收敛，例如最大关键组件的直径。此外，我们的结果为随机度量空间的紧凑性提供了足够的条件，而随机度量空间的紧凑性是在重尾状态下临界簇的缩放限制。
We establish the global lower mass-bound property for the largest connected components in the critical window for the configuration model when the degree distribution has an infinite third moment. The scaling limit of the critical percolation clusters, viewed as measured metric spaces, was established in [7] with respect to the Gromov-weak topology. Our result extends those scaling limit results to the stronger Gromov-Hausdorff-Prokhorov topology under slightly stronger assumptions on the degree distribution. This implies the distributional convergence of global functionals such as the diameter of the largest critical components. Further, our result gives a sufficient condition for compactness of the random metric spaces that arise as scaling limits of critical clusters in the heavy-tailed regime.
