title: Steady state and mean recurrence time for random walks on stochastic temporal networks.
abstract: 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 reinitialized only on the link that has been used the 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.
authors: Department of Mathematical Informatics, University of Tokyo, Tokyo, Japan and JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan.
authors: Leo
authors: L
authors: Speidel
authors: Department of Mathematics/Naxys, University of Namur, Namur, Belgium.
authors: Renaud
authors: R
authors: Lambiotte
authors: Department of Mathematical Informatics, University of Tokyo, Tokyo, Japan and Institute of Industrial Science, University of Tokyo, Tokyo, Japan.
authors: Kazuyuki
authors: K
authors: Aihara
authors: Department of Engineering Mathematics, University of Bristol, Bristol, UK and CREST, JST, Saitama, Japan.
authors: Naoki
authors: N
authors: Masuda