Power laws in zero-range processes on random networks

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.