Sharp mean-field estimates for the repulsive log gas in any dimension
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913915046199296 |
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| author | Delgadino, Matias G. Gvalani, Rishabh S. |
| author_facet | Delgadino, Matias G. Gvalani, Rishabh S. |
| contents | We prove sharp estimates for the mean-field limit of weakly interacting diffusions with repulsive logarithmic interaction in arbitrary dimension. More precisely, we show that the associated partition function is uniformly bounded in the number of particles $N$ for an arbitrary bounded base measure. Combined with the modulated free energy method, this amounts to a logarithmic improvement in $N$ of the current best available closeness estimates in the literature. Our arguments are inspired by and borrow ideas from Nelson's classical construction of the $φ^4_2$ Euclidean quantum field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp mean-field estimates for the repulsive log gas in any dimension Delgadino, Matias G. Gvalani, Rishabh S. Probability Analysis of PDEs We prove sharp estimates for the mean-field limit of weakly interacting diffusions with repulsive logarithmic interaction in arbitrary dimension. More precisely, we show that the associated partition function is uniformly bounded in the number of particles $N$ for an arbitrary bounded base measure. Combined with the modulated free energy method, this amounts to a logarithmic improvement in $N$ of the current best available closeness estimates in the literature. Our arguments are inspired by and borrow ideas from Nelson's classical construction of the $φ^4_2$ Euclidean quantum field theory. |
| title | Sharp mean-field estimates for the repulsive log gas in any dimension |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2506.22083 |