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      Random walk of second class particles in product shock measures

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          Abstract

          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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          Most cited references 14

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          Interaction of Markov processes

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            Hydrodynamic limit for attractive particle systems on 417-1417-1417-1

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              Processus des misanthropes

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                Author and article information

                Journal
                16 September 2009
                2010-01-20
                10.1007/s10955-010-9933-8
                0909.3071

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                60K35; 82C23
                J. Stat. Phys. 139:(2) (2010) 252-279
                Minor changes after referees' comments
                math.PR cond-mat.stat-mech

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