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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.09123 |
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| _version_ | 1866911201875722240 |
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| author | Auricchio, Gennaro Toscani, Giuseppe |
| author_facet | Auricchio, Gennaro Toscani, Giuseppe |
| contents | We study the rate of convergence to equilibrium of the solutions to Fokker-Planck type equations with linear drift by means of Cramér and Energy distances, which have been recently widely used in problems related to AI, in particular for tasks related to machine learning. In all cases in which the Fokker-Planck type equations can be treated through these distances, it is shown that the rate of decay is improved with respect to known results which are based on the decay of relative entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09123 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy distance and evolution problems: a promising tool for kinetic equations Auricchio, Gennaro Toscani, Giuseppe Analysis of PDEs Physics and Society We study the rate of convergence to equilibrium of the solutions to Fokker-Planck type equations with linear drift by means of Cramér and Energy distances, which have been recently widely used in problems related to AI, in particular for tasks related to machine learning. In all cases in which the Fokker-Planck type equations can be treated through these distances, it is shown that the rate of decay is improved with respect to known results which are based on the decay of relative entropy. |
| title | Energy distance and evolution problems: a promising tool for kinetic equations |
| topic | Analysis of PDEs Physics and Society |
| url | https://arxiv.org/abs/2510.09123 |