Journal of Statistical Physics

, Volume 139, Issue 2, pp 252–279 | Cite as

Random Walk of Second Class Particles in Product Shock Measures

  • Márton BalázsEmail author
  • György Farkas
  • Péter Kovács
  • Attila Rákos


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.


Interacting particle systems Second class particle Shock measure Exact solution Asymmetric simple exclusion Zero range process Bricklayers process Branching coalescing random walks 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Márton Balázs
    • 1
    Email author
  • György Farkas
    • 2
  • Péter Kovács
    • 2
  • Attila Rákos
    • 3
  1. 1.Department of Stochastics, Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Budapest University of Technology and EconomicsBudapestHungary
  3. 3.Research Group for Condensed Matter Physics, Hungarian Academy of SciencesBudapest University of Technology and EconomicsBudapestHungary

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