Classes of random walks on temporal networks with competing timescales

Random walks find applications in many areas of science and are the heart of
essential network analytic tools. When defined on temporal networks, even basic
random walk models may exhibit a rich spectrum of behaviours, due to the
co-existence of different timescales in the system. Here, we introduce random
walks on general stochastic temporal networks allowing for lasting
interactions, with up to three competing timescales. We then compare the mean
resting time and stationary state of different models. We also discuss the
accuracy of the mathematical analysis depending on the random walk model and
the structure of the underlying network, and pay particular attention to the
emergence of non-Markovian behaviour, even when all dynamical entities are
governed by memoryless distributions.