Construction of the factorized steady state distribution in models of mass transport

Royce K.P. Zia 1, Martin R. Evans 2, Satya N. Majumdar 3

Journal of Statistical Mechanics: Theory and Experiment 1 (2004) L10001

For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary distribution is factorized. In cases where the answer is affirmative, we provide an explicit method for constructing the single-site weight function. As an illustration of the power of this approach, previously known results on the Zero-range process and Asymmetric random average process are recovered in a few lines. We also construct new models, namely a generalized Zero-range process and a binomial chipping model, which have factorized steady states.

  • 1. Department of Physics and Center for Stochastic Processes in Science and Engineering,
    Virgina Tech
  • 2. School of Physics,
    University of Edinburgh
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud