On Convergence to Equilibrium of Infinite Closed Jackson Networks

#### D. Khmelev

2005, v.11, Issue 3, 467-488

ABSTRACT

This paper studies an infinite asymmetric close Jackson network, which is a generalization of a zero range interaction process at Bose - Einstein speeds. The network is expected to approach equilibrium if deterministic initial configuration has density. It is shown that in some networks on $\math {N}$ this is indeed the case, moreover, there exist irregular initial configurations such that marginal distributions of the network oscillate with time. However one can construct examples of two networks on $\math {Z}$ such that their finite restrictions share the same invariant distributions, while the infinite networks starting from the same initial configuration converge to different invariant distributions.

Keywords: interacting particle systems,zero range process,convergence to equilibrium