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Asymmetric attractive zero-range processes with particle destruction at the origin

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  • Erignoux, Clément
  • Simon, Marielle
  • Zhao, Linjie

Abstract

We investigate the macroscopic behavior of asymmetric attractive zero-range processes on Z where particles are destroyed at the origin at a rate of order Nβ, where β∈R and N∈N is the scaling parameter. We prove that the hydrodynamic limit of this particle system is described by the unique entropy solution of a hyperbolic conservation law, supplemented by a boundary condition depending on the range of β. Namely, if β⩾0, then the boundary condition prescribes the particle current through the origin, whereas if β<0, the destruction of particles at the origin has no macroscopic effect on the system and no boundary condition is imposed at the hydrodynamic limit.

Suggested Citation

  • Erignoux, Clément & Simon, Marielle & Zhao, Linjie, 2023. "Asymmetric attractive zero-range processes with particle destruction at the origin," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 1-33.
    • Handle: RePEc:eee:spapps:v:159:y:2023:i:c:p:1-33
    DOI: 10.1016/j.spa.2023.01.015
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