Slow relaxation dynamics and aging in random walks on activity driven temporal networks

We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [Perra $\mathit{\text{et}}\mathit{\text{al.}}$ Sci. Rep. srep00469 (2012)]. For realistic activity distributions with a power-law form, we observe the presence of a very slow relaxation dynamics compatible with aging effects. A theoretical description of this processes in achieved by means of a mapping to Bouchaud’s trap model. The mapping highlights the profound difference in the dynamics of the random walks according to the value of the exponent $\gamma$ in the activity distribution.