  The random walk process underlies the description of a large number of real
world phenomena. Here we provide the study of random walk processes in time
varying networks in the regime of time-scale mixing; i.e. when the network
connectivity pattern and the random walk process dynamics are unfolding on the
same time scale. We consider a model for time varying networks created from the
activity potential of the nodes, and derive solutions of the asymptotic
behavior of random walks and the mean first passage time in undirected and
directed networks. Our findings show striking differences with respect to the
well known results obtained in quenched and annealed networks, emphasizing the
effects of dynamical connectivity patterns in the definition of proper
strategies for search, retrieval and diffusion processes in time-varying
networks
