Random walk on temporal networks with lasting edges

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We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting time, the up time, and the down time of the edges. We first propose a comprehensive analytical and numerical treatment on directed acyclic graphs. Once cycles are allowed in the network, non-Markovian trajectories may emerge, remarkably even if the walker and the evolution of the network edges are governed by memoryless Poisson processes. We then introduce a general analytical framework to characterize such non-Markovian walks and validate our findings with numerical simulations.
Original languageEnglish
Article number052307
Number of pages16
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - 20 Nov 2018


  • continuous time random walk
  • time varying network
  • diffusion and random walk
  • complex networks


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