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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M. Balázs was partially supported by the Hungarian Scientific Research Fund (OTKA) grants K-60708, F-67729, by the Bolyai Scholarship of the Hungarian Academy of Sciences, and by Morgan Stanley Mathematical Modeling Center.
A. Rákos acknowledges financial support of the Hungarian Scientific Research Fund (OTKA) grants PD-72604, PD-78433 and from the Bolyai Scholarship of the Hungarian Academy of Sciences.
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Balázs, M., Farkas, G., Kovács, P. et al. Random Walk of Second Class Particles in Product Shock Measures. J Stat Phys 139, 252–279 (2010). https://doi.org/10.1007/s10955-010-9933-8
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DOI: https://doi.org/10.1007/s10955-010-9933-8