论文标题
给定度的密集随机图上的渗透
Percolation on dense random graphs with given degrees
论文作者
论文摘要
在本文中，我们研究了具有两个随机性源的随机图的最大连接组件的顺序：首先，从具有给定度序列的所有图中随机选择该图，然后应用键合渗透。在两个随机性来源方面，我们无法对所有此类程度的序列进行分类，而是最大组成部分的几个新阈值现象。我们还提供了一个度序列的示例，最大成分的顺序在渗透参数方面经历了无界数量的跳跃，从而产生了没有渗透就无法观察到的行为。
In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied. Far from being able to classify all such degree sequences, we exhibit several new threshold phenomena for the order of the largest component in terms of both sources of randomness. We also provide an example of a degree sequence for which the order of the largest component undergoes an unbounded number of jumps in terms of the percolation parameter, giving rise to a behavior that cannot be observed without percolation.
