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

TL;DR

This paper studies how random walks on activity-driven temporal networks relax slowly over time, revealing aging effects and differences in dynamics based on activity distribution exponents, using a Bouchaud trap model mapping.

Contribution

It introduces a theoretical framework linking slow relaxation and aging in random walks on activity-driven networks via a Bouchaud trap model mapping.

Findings

Slow relaxation dynamics observed in networks with power-law activity distributions

Aging effects are present in the relaxation process

Dynamics vary significantly with the activity distribution exponent 

Abstract

We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [Perra \textit{et 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.