Random walk of second class particles in product shock measures

Details Random walk of second class particles in product shock measures Random walk of second class particles in product shock measures

2009-09-16

arxiv.org/abs/0909.3071v3

J. Stat. Phys. 139:(2) (2010) 252-279

Mathematics

Probability

Minor changes after referees' comments

Scientific paper

10.1007/s10955-010-9933-8

We consider shock measures in a class of conserving stochastic particle systems on Z. These shock measures have a product structure with a step-like density profile and include a second class particle at the shock position. We show for the asymmetric simple exclusion process, for the exponential bricklayers' process, and for a generalized zero range process, that under certain conditions these shocks, and therefore the second class particles, perform a simple random walk. Some previous results, including random walks of product shock measures and stationary shock measures seen from a second class particle, are direct consequences of our more general theorem. Multiple shocks can also be handled easily in this framework. Similar shock structure is also found in a nonconserving model, the branching coalescing random walk, where the role of the second class particle is played by the rightmost (or leftmost) particle.

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