随机时态网络上随机游动的稳态和平均递归时间
Steady state and mean recurrence time for random walks on stochastic temporal networks
摘要：
随机游走是网络上的基本扩散过程，在搜索、导航、排名和社区检测等方面都有应用。最近认识到的重要性，时间方面的网络刺激的研究随机游动的时间网络。在这里，我们从理论上研究了两种类型的事件驱动的随机游动的随机时间网络模型，产生任意分布的interevent-times。在所谓的主动随机游走中，在步行者的每次移动时，在所有链路上重新初始化间隔时间。在所谓的被动随机游走中，只在上次使用过的链路上重新初始化间隔时间，这是一种相关随机游走。我们发现，对于被动随机游动，定态总是均匀密度。相反，对于主动随机游动，它的增加或减少取决于间隔时间的分布的节点的度。对于主动和被动随机游动，节点的平均递归时间与度成反比。此外，对于主动随机游动和被动随机游动，平均重现时间分别取决于或不取决于间隔时间的分布。
英文摘要：
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of random walks on temporal networks. Here we theoretically study two types of event-driven random walks on a stochastic temporal network model that produces arbitrary distributions of interevent-times. In the so-called active random walk, the interevent-time is reinitialized on all links upon each movement of the walker. In the so-called passive random walk, the interevent-time is only reinitialized on the link that has been used last time, and it is a type of correlated random walk. We find that the steady state is always the uniform density for the passive random walk. In contrast, for the active random walk, it increases or decreases with the node's degree depending on the distribution of interevent-times. The mean recurrence time of a node is inversely proportional to the degree for both active and passive random walks. Furthermore, the mean recurrence time does or does not depend on the distribution of interevent-times for the active and passive random walks, respectively.
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