Hydrodynamic limit for asymmetric simple exclusion with accelerated boundaries
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913477997625344 |
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| author | Xu, Lu |
| author_facet | Xu, Lu |
| contents | We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional finite lattice $\{1,2,\ldots,N\}$. The particles can be created/annihilated at the boundaries with given rates. These rates are $L^\infty$ functions of time and are independent of the jump rates in the bulk. The boundary dynamics is modified by a factor $N^θ$ with $θ>0$. We study the hydrodynamic limit for the particle density profile under the hyperbolic space-time scale. The macroscopic equation is given by (inviscid) Burgers equation with Dirichlet type boundaries that is characterized by the boundary entropy. A grading scheme is developed to control the formulation of boundary layers on the microscopic level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_09345 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit for asymmetric simple exclusion with accelerated boundaries Xu, Lu Probability Mathematical Physics 60K35, 82C22 We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional finite lattice $\{1,2,\ldots,N\}$. The particles can be created/annihilated at the boundaries with given rates. These rates are $L^\infty$ functions of time and are independent of the jump rates in the bulk. The boundary dynamics is modified by a factor $N^θ$ with $θ>0$. We study the hydrodynamic limit for the particle density profile under the hyperbolic space-time scale. The macroscopic equation is given by (inviscid) Burgers equation with Dirichlet type boundaries that is characterized by the boundary entropy. A grading scheme is developed to control the formulation of boundary layers on the microscopic level. |
| title | Hydrodynamic limit for asymmetric simple exclusion with accelerated boundaries |
| topic | Probability Mathematical Physics 60K35, 82C22 |
| url | https://arxiv.org/abs/2108.09345 |