Patricia Goncalves
Published 2009-12-03, updated 2012-03-01Version 4
We consider the one-dimensional totally asymmetric zero-range process starting from a step decreasing profile leading in the hydrodynamic limit to the rarefaction fan of the associate hydrodynamic equation. Under that initial condition, we show that the weighted sum of joint probabilities for second class particles sharing the same site, is convergent and we compute its limit. We derive the Law of Large Numbers for the position of a second class particle initially at the origin under the initial state in which all positive sites are empty and all negative sites are occupied and also for a slight perturbation of the invariant state.
Comments: 15 pages 3 figures. This paper has been improved and the title has also changed to On the asymmetric zero-range in the rarefaction fan
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