A criterion on the free energy for log-Sobolev inequalities in mean-field particle systems
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| Format: | Preprint |
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2025
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| _version_ | 1866913768772993024 |
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| author | Bauerschmidt, R. Bodineau, T. Dagallier, B. |
| author_facet | Bauerschmidt, R. Bodineau, T. Dagallier, B. |
| contents | For a class of mean-field particle systems, we formulate a criterion in terms of the free energy that implies uniform bounds on the log-Sobolev constant of the associated Langevin dynamics. For certain double-well potentials with quadratic interaction, the criterion holds up to the critical temperature of the model, and we also obtain precise asymptotics on the decay of the log-Sobolev constant when approaching the critical point. The criterion also applies to ``diluted'' mean-field models defined on sufficiently dense, possibly random graphs. We further generalize the criterion to non-quadratic interactions that admit a mode decomposition. The mode decomposition is different from the scale decomposition of the Polchinski flow we used for short-range spin systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_24372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A criterion on the free energy for log-Sobolev inequalities in mean-field particle systems Bauerschmidt, R. Bodineau, T. Dagallier, B. Probability Mathematical Physics Functional Analysis For a class of mean-field particle systems, we formulate a criterion in terms of the free energy that implies uniform bounds on the log-Sobolev constant of the associated Langevin dynamics. For certain double-well potentials with quadratic interaction, the criterion holds up to the critical temperature of the model, and we also obtain precise asymptotics on the decay of the log-Sobolev constant when approaching the critical point. The criterion also applies to ``diluted'' mean-field models defined on sufficiently dense, possibly random graphs. We further generalize the criterion to non-quadratic interactions that admit a mode decomposition. The mode decomposition is different from the scale decomposition of the Polchinski flow we used for short-range spin systems. |
| title | A criterion on the free energy for log-Sobolev inequalities in mean-field particle systems |
| topic | Probability Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2503.24372 |