Eur. Phys. J. B 65, 565-570 (2008)
https://doi.org/10.1140/epjb/e2008-00361-0

Power laws in zero-range processes on random networks

¹ Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
² Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30059 Kraków, Poland
³ Mark Kac Complex Systems Research Centre, Jagellonian University, Kraków, Poland
⁴ Centre for Theoretical Sciences (NTZ), Universität Leipzig, Emil-Fuchs-Straße 1, 04105 Leipzig, Germany

Corresponding author: ^a bwaclaw@googlemail.com

Received: 3 March 2008
Revised: 7 August 2008
Published online: 25 September 2008

Abstract

We study statistical properties of a zero-range process (ZRP) on random networks. We derive an analytic expression for the distribution of particles (also called node occupation distribution) in the steady state of the ZRP in the ensemble of uncorrelated random graphs. We analyze the dependence of this distribution on the node-degree distribution. In particular, we show that when the degree distribution is tuned properly, one can obtain scale-free fluctuations in the distribution of particles. Such fluctuations lead to a power law in the distribution of particles, just like in the ZRP with the hopping rate u(m) = 1+b/m on homogeneous graphs.