Asymmetric attractive zero-range processes with particle destruction at the origin
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866915093700149248 |
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| author | Simon, Marielle Zhao, Linjie Erignoux, Clément |
| author_facet | Simon, Marielle Zhao, Linjie Erignoux, Clément |
| contents | We investigate the macroscopic behavior of asymmetric attractive zero-range processes on $\mathbb{Z}$ where particles are destroyed at the origin at a rate of order $N^β$, where $β\in \mathbb{R}$ and $N\in\mathbb{N}$ 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 $β\geqslant 0$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_04133 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Asymmetric attractive zero-range processes with particle destruction at the origin Simon, Marielle Zhao, Linjie Erignoux, Clément Probability Mathematical Physics We investigate the macroscopic behavior of asymmetric attractive zero-range processes on $\mathbb{Z}$ where particles are destroyed at the origin at a rate of order $N^β$, where $β\in \mathbb{R}$ and $N\in\mathbb{N}$ 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 $β\geqslant 0$, 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. |
| title | Asymmetric attractive zero-range processes with particle destruction at the origin |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2109.04133 |