2006/02/23 by M. R. Evans, Satya N. Majumdar, R. K. P. Zia · 3 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/39/18/006
published as J. Phys. A: Math. Gen, Vol. 39, 4859-4873 (2006) · 17 pages 1 figure
arxiv created 2006/02/23 · openalex publication_date 2006/04/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We study a general mass transport model on an arbitrary graph consisting of L nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the zero-range process and the asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorizable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for d -dimensional hypercubic lattices with random sequential dynamics.