A consistency-stability approach to scaling limits of zero-range processes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917876140605440 |
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| author | Marahrens, Daniel Menegaki, Angeliki Mouhot, Clément |
| author_facet | Marahrens, Daniel Menegaki, Angeliki Mouhot, Clément |
| contents | We propose a simple quantitative method for studying the hydrodynamic limit of interacting particle systems on lattices. It is applied to the diffusive scaling of the symmetric Zero-Range Process (in dimensions one and two). The rate of convergence is estimated in a Monge-Kantorovich distance asymptotic to the L^1 stability estimate of Kruzkhov, as well as in relative entropy; and it is uniform in time. The method avoids the use of the so-called ``block estimates''. It is based on a modulated Monge-Kantorovich distance estimate and microscopic stability properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A consistency-stability approach to scaling limits of zero-range processes Marahrens, Daniel Menegaki, Angeliki Mouhot, Clément Probability Mathematical Physics Analysis of PDEs We propose a simple quantitative method for studying the hydrodynamic limit of interacting particle systems on lattices. It is applied to the diffusive scaling of the symmetric Zero-Range Process (in dimensions one and two). The rate of convergence is estimated in a Monge-Kantorovich distance asymptotic to the L^1 stability estimate of Kruzkhov, as well as in relative entropy; and it is uniform in time. The method avoids the use of the so-called ``block estimates''. It is based on a modulated Monge-Kantorovich distance estimate and microscopic stability properties. |
| title | A consistency-stability approach to scaling limits of zero-range processes |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2412.16714 |