具有有限三阶矩的临界非齐次随机图的标度极限
Scaling limits for critical inhomogeneous random graphs with finite third moments
摘要：
当度指数$τ$满足$τ>4$时，我们确定了非齐次随机图临界点最大分量大小的标度极限。我们看到，（重新标度）组件的大小收敛到一个非齐次布朗运动的行程长度，扩展\cite{Aldo97}的结果。我们在很大程度上依赖于鞅收敛技巧和（上）鞅的集中性质。本文是一个计划的一部分，研究所谓的秩-1的非齐次随机图的临界行为在\cite{Hofs09a}开始。
英文摘要：
We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent $τ$ satisfies $τ>4$. We see that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, extending results of \cite{Aldo97}. We rely heavily on martingale convergence techniques, and concentration properties of (super)martingales. This paper is part of a programme to study the critical behavior in inhomogeneous random graphs of so-called rank-1 initiated in \cite{Hofs09a}.
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