Size of chaos for Gibbs measures of mean field interacting diffusions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909871963635712 |
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| author | Ren, Zhenjie Wang, Songbo |
| author_facet | Ren, Zhenjie Wang, Songbo |
| contents | We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle interaction forces that are unbounded at infinity, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach provides a unified framework for both the flat semi-convex and displacement convex cases. Additionally, we establish sharp chaos bounds for the quartic Curie-Weiss model in the sub-critical regime, demonstrating the generality of this method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_14236 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Size of chaos for Gibbs measures of mean field interacting diffusions Ren, Zhenjie Wang, Songbo Probability Mathematical Physics 82B21 (Primary) 60F05, 37L15 (Secondary) We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle interaction forces that are unbounded at infinity, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach provides a unified framework for both the flat semi-convex and displacement convex cases. Additionally, we establish sharp chaos bounds for the quartic Curie-Weiss model in the sub-critical regime, demonstrating the generality of this method. |
| title | Size of chaos for Gibbs measures of mean field interacting diffusions |
| topic | Probability Mathematical Physics 82B21 (Primary) 60F05, 37L15 (Secondary) |
| url | https://arxiv.org/abs/2411.14236 |