Wasserstein-infinity stability and mean field limit of discrete interaction energy minimizers
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911968609173504 |
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| author | Shu, Ruiwen |
| author_facet | Shu, Ruiwen |
| contents | In this paper we give a quantitative stability result for the discrete interaction energy on the multi-dimensional torus, for the periodic Riesz potential. It states that if the number of particles $N$ is large and the discrete interaction energy is low, then the particle distribution is necessarily close to the uniform distribution (i.e., the continuous energy minimizer) in the Wasserstein-infinity distance. As a consequence, we obtain a quantitative mean field limit of interaction energy minimizers in the Wasserstein-infinity distance. The proof is based on the application of the author's previous joint work with J. Wang on the stability of continuous energy minimizer, together with a new mollification trick for the empirical measure in the case of singular interaction potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wasserstein-infinity stability and mean field limit of discrete interaction energy minimizers Shu, Ruiwen Analysis of PDEs Classical Analysis and ODEs 52C35, 74G65 In this paper we give a quantitative stability result for the discrete interaction energy on the multi-dimensional torus, for the periodic Riesz potential. It states that if the number of particles $N$ is large and the discrete interaction energy is low, then the particle distribution is necessarily close to the uniform distribution (i.e., the continuous energy minimizer) in the Wasserstein-infinity distance. As a consequence, we obtain a quantitative mean field limit of interaction energy minimizers in the Wasserstein-infinity distance. The proof is based on the application of the author's previous joint work with J. Wang on the stability of continuous energy minimizer, together with a new mollification trick for the empirical measure in the case of singular interaction potentials. |
| title | Wasserstein-infinity stability and mean field limit of discrete interaction energy minimizers |
| topic | Analysis of PDEs Classical Analysis and ODEs 52C35, 74G65 |
| url | https://arxiv.org/abs/2407.18395 |