Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917884836446208 |
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| author | Carrillo, José Antonio Guo, Shuchen Holzinger, Alexandra |
| author_facet | Carrillo, José Antonio Guo, Shuchen Holzinger, Alexandra |
| contents | We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting particle systems approximating attractive/repulsive singular potentials up to Newtonian/Coulomb singularities without additional cut-off on the particle level. The first step is to make use of the relative entropy between the joint distribution of the particle system and an approximated limiting aggregation-diffusion system. A crucial argument in the proof is to show convergence in probability by a stopping time argument. The second step is to obtain a quantitative convergence rate to the limiting aggregation-diffusion system from the approximated PDE system. This is shown by evaluating a combination of relative entropy and $L^2$-distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity Carrillo, José Antonio Guo, Shuchen Holzinger, Alexandra Probability Analysis of PDEs We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting particle systems approximating attractive/repulsive singular potentials up to Newtonian/Coulomb singularities without additional cut-off on the particle level. The first step is to make use of the relative entropy between the joint distribution of the particle system and an approximated limiting aggregation-diffusion system. A crucial argument in the proof is to show convergence in probability by a stopping time argument. The second step is to obtain a quantitative convergence rate to the limiting aggregation-diffusion system from the approximated PDE system. This is shown by evaluating a combination of relative entropy and $L^2$-distance. |
| title | Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2501.03087 |