论文标题
爆炸性渗透中的多重和不对称尺度
Multiple and Asymmetric Scalings in Explosive Percolation
论文作者
论文摘要
Achlioptas过程中的爆炸性渗透最近引起了很多研究的关注。从基于事件的集合中的广泛仿真中，我们发现，在$ 2 $到$ 6 $的维度上，在随机图上，Achlioptas流程都具有两个缩放窗口和多个分形结构。这些多个量表的混合成功地解释了常规集合中先前观察到的异常现象，此外，现在通过基于事件的方法以高精度确定正确的关键指数。多个量表和整体不等式可能会为其他统计系统带来新的见解。
Explosive percolation in the Achlioptas process has recently attracted much research attention. From extensive simulations in an event-based ensemble, we find that, in dimensions from $2$ to $6$ and on random graphs, the Achlioptas processes all have two scaling windows and multiple fractal structures. The mixing of these multiple scalings successfully explains the previously observed anomalous phenomena in the conventional ensemble, and, moreover, correct critical exponents are now determined with a high precision by the event-based method. The multiple scalings and the ensemble inequivalence may bring new insights for other statistical systems.
