  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.
