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Register a new userRandom walks in non-Poissoinan activity driven temporal networks
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Added by
Romualdo Pastor-Satorras
Publication date
2019
fields
Physics
and research's language is
English
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The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an inter-event time between consecutive interactions showing a heavy-tailed distribution. In particular, empirical data has shown that the bursty dynamics of temporal networks can have deep consequences on the behavior of the dynamical processes running on top of them. Here, we study the case of random walks, as a paradigm of diffusive processes, unfolding on temporal networks generated by a non-Poissonian activity driven dynamics. We derive analytic expressions for the steady state occupation probability and first passage time distribution in the infinite network size and strong aging limits, showing that the random walk dynamics on non-Markovian networks are fundamentally different from what is observed in Markovian networks. We found a particularly surprising behavior in the limit of diverging average inter-event time, in which the random walker feels the network as homogeneous, even though the activation probability of nodes is heterogeneously distributed. Our results are supported by extensive numerical simulations. We anticipate that our findings may be of interest among the researchers studying non-Markovian dynamics of time-evolving complex topologies.
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Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting nodes. Using a renewal approach, we derive exact expressions of the occupation probability of the walker in each node and mean-field first-passage time between arbitrary two nodes. All the results are relevant to the spectral properties of the transition matrix in the absence of resetting. We demonstrate our results on circular networks, stochastic block models, and Barabasi-Albert scale-free networks, and find the advantage of the resetting processes to multiple resetting nodes in global searching on such networks.
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