Random walk of second class particles in product shock measures

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.

Minor changes after referees' comments

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Cited by in corpus (10)

• A reverse duality for the ASEP with open boundaries
• Compact Waves in Microscopic Nonlinear Diffusion
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• Self-duality and shock dynamics in the $n$-component priority ASEP
• On the phase transition in the sublattice TASEP with stochastic blockage
• Duality relations for the ASEP conditioned on a low current
• Fluctuation bounds in the exponential bricklayers process
• Q-zero range has random walking shocks
• Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems
• Universal scaling for second class particles in a one-dimensional misanthrope process