论文标题
弱多重渗透的外在临界行为
Exotic Critical Behavior of Weak Multiplex Percolation
论文作者
论文摘要
我们描述了弱的多路复用渗透的临界行为，将渗透对多路复用或相互依存网络的概括。节点可以通过引用相邻节点来确定其活动状态或非活动状态。对于渗透到多重网络（相互连接的簇）的渗透概括的情况并非如此，这需要在巨型相互连接的分量中的任何两个顶点之间的每个层中的互连路径。我们研究了在弱渗透规则下，活性节点的巨大相互联系的成分的出现，发现了几种非典型现象。在两层中，巨型成分以连续相变的形式出现，但二次增长高于临界阈值。在三个或多个层中，发生不连续的杂种跃迁，类似于巨型相互连接的分量中的杂种。在具有偏差的powerlaw学位分布的网络中，由衰减指数$γ$定义，不连续性消失了，但在$γ= 1.5 $中，三层中的损失为1.5 $，更一般而言，$γ= 1+ 1/（m-1）$ in $ m $ layers。
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several non-typical phenomena. In two layers, the giant component emerges with a continuos phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent $γ$, the discontinuity vanishes but at $γ=1.5$ in three layers, more generally at $γ= 1+ 1/(M-1)$ in $M$ layers.
