随机度受限过程的局部极限

Balázs Ráth, Márton Szőke, Lutz Warnke
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引用次数: 0

摘要

在本文中,我们证明了随机度约束过程(具有度约束的时间演化随机图模型)具有局部弱极限,前提是底层主图是高度几乎规则的。此外,我们通过将耦合论证与对某种递归树过程的分析相结合,将极限对象识别为多类型分支过程。我们还利用光谱特性,给出了所谓随机 $d$ 过程中巨型成分出现的临界时间的渐近展开,解决了 Warnke 和 Wormald 提出的一个关于大 $d$ 的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Local limit of the random degree constrained process
In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover, identify the limit object as a multi-type branching process, by combining coupling arguments with the analysis of a certain recursive tree process. Using a spectral characterization, we also give an asymptotic expansion of the critical time when the giant component emerges in the so-called random $d$-process, resolving a problem of Warnke and Wormald for large $d$.
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