Eur. Phys. J. B (2015) 88: 38
https://doi.org/10.1140/epjb/e2014-50801-1

Regular Article

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

¹ Departamento de Física, Universidade Federal de Viçosa, 36571-000, Viçosa – MG, Brazil
² Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain

^a e-mail: angelica.mata@ufv.br

Received: 17 November 2014
Received in final form: 15 December 2014
Published online: 4 February 2015

Abstract

We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [N. Perra, B. Gonçalves, R. Pastor-Satorras, A. Vespignani, Sci. Rep. 2, 469 (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 γ in the activity distribution.