Explosive Percolation Is Continuous
Explosive Percolation Is Continuous
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DOI：
10.1126/science.1206241
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发表时间：
2011-07-15
期刊：
影响因子：
56.9
通讯作者：
Warnke, Lutz
中科院分区：
文献类型：
--
作者：
Riordan, Oliver;Warnke, Lutz
“爆炸渗透”被认为发生在一个进化的网络中，当一个宏观的连接组件在许多步骤中出现时，这个步骤比系统的大小要小得多。最近基于模拟的预测表明，某些Achlioptas过程（对Erdos和Renyi经典平均场增长模型进行了大量研究的局部修正）表现出这种现象，在尺度极限上经历了不连续的相变。我们表明，事实上，所有的Achlioptas过程都有连续的相变，尽管相关的模型中采样的节点数量可能随着网络大小的增长而增长，但确实可以表现出爆炸性的渗透。
"Explosive percolation" is said to occur in an evolving network when a macroscopic connected component emerges in a number of steps that is much smaller than the system size. Recent predictions based on simulations suggested that certain Achlioptas processes (much-studied local modifications of the classical mean-field growth model of Erdos and Renyi) exhibit this phenomenon, undergoing a phase transition that is discontinuous in the scaling limit. We show that, in fact, all Achlioptas processes have continuous phase transitions, although related models in which the number of nodes sampled may grow with the network size can indeed exhibit explosive percolation.