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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.19447 |
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| _version_ | 1866909754959331328 |
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| author | Araújo, Oslenne Gonçalves, Patrícia Neumann, Adriana Ricciuti, Maria Chiara |
| author_facet | Araújo, Oslenne Gonçalves, Patrícia Neumann, Adriana Ricciuti, Maria Chiara |
| contents | We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that scale like $N^{-θ}$ with $θ\ge1$. Under mild assumptions on the jump rate and the sequence of initial measures, we show that the empirical density evolves on the diffusive scale according to a nonlinear heat equation, with boundary conditions reflecting the strength of the reservoirs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary Araújo, Oslenne Gonçalves, Patrícia Neumann, Adriana Ricciuti, Maria Chiara Probability We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that scale like $N^{-θ}$ with $θ\ge1$. Under mild assumptions on the jump rate and the sequence of initial measures, we show that the empirical density evolves on the diffusive scale according to a nonlinear heat equation, with boundary conditions reflecting the strength of the reservoirs. |
| title | Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary |
| topic | Probability |
| url | https://arxiv.org/abs/2508.19447 |