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

Clément Erignoux, Marielle Simon and Linjie Zhao

Stochastic Processes and their Applications, 2023, vol. 159, issue C, 1-33

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.

Keywords: asymmetric zero-range process; boundary condition; hyperbolic conservation law; hydrodynamic limit; attractiveness (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.01.015

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