Random walk on temporal networks with lasting edges

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 down-time of edges activation. 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.