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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.10440 |
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| _version_ | 1866917777100505088 |
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| author | Chewi, Sinho Nitanda, Atsushi Zhang, Matthew S. |
| author_facet | Chewi, Sinho Nitanda, Atsushi Zhang, Matthew S. |
| contents | We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles $N$. Our proof proceeds by establishing the existence of a Lipschitz transport map from the standard Gaussian measure via the reverse heat flow of Kim and Milman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy Chewi, Sinho Nitanda, Atsushi Zhang, Matthew S. Probability We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles $N$. Our proof proceeds by establishing the existence of a Lipschitz transport map from the standard Gaussian measure via the reverse heat flow of Kim and Milman. |
| title | Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy |
| topic | Probability |
| url | https://arxiv.org/abs/2409.10440 |