BIBTEX ENTRY



@article{ESZ23-1,
title = {Asymmetric attractive zero-range processes with particle destruction at the origin},
journal = {Stochastic Processes and their Applications},
volume = {159},
pages = {1-33},
year = {2023},
issn = {0304-4149},
doi = {https://doi.org/10.1016/j.spa.2023.01.015},
url = {https://www.sciencedirect.com/science/article/pii/S0304414923000248},
author = {Clément Erignoux and Marielle Simon and Linjie Zhao},
keywords = {asymmetric zero-range process, boundary condition, hyperbolic conservation law, hydrodynamic limit, attractiveness},
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.}
}




BIBITEM ENTRY



\bibitem{ESZ23-1}
C. Erignoux, M. Simon and L. Zhao,
\emph{Asymmetric attractive zero-range processes with particle destruction at the origin},  
Stochastic Processes and their Applications, 
Vol. 159, pp 1--33 (2023).