Power laws in zero-range processes on random networks

TL;DR

This paper derives an analytic expression for the steady-state particle distribution in zero-range processes on random networks, showing how tuning degree distributions can produce scale-free, power-law fluctuations similar to those on homogeneous graphs.

Contribution

It provides a new analytic framework for understanding particle distributions in ZRP on random networks, linking degree distributions to power-law behaviors.

Findings

Power-law particle distributions can be achieved by tuning degree distributions.

Analytic expression for steady-state distribution in ZRP on uncorrelated random graphs.

Scale-free fluctuations emerge under specific degree distribution conditions.

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.