Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912912689332224 |
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| author | Bodineau, Thierry Bris, Pierre Le |
| author_facet | Bodineau, Thierry Bris, Pierre Le |
| contents | We consider a tagged particle in mean field interaction with a free gas of density N at equilibrium. In dimensions $d\geq4$, we prove the convergence of its trajectory, as N goes to infinity, to the one of a diffusion process associated with the linear Landau equation. The proof of the convergence of the martingale problem relies on two key ingredients: long time stability results of the microscopic dynamics, and controls on the probability of particle recollisions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas Bodineau, Thierry Bris, Pierre Le Probability Mathematical Physics Analysis of PDEs We consider a tagged particle in mean field interaction with a free gas of density N at equilibrium. In dimensions $d\geq4$, we prove the convergence of its trajectory, as N goes to infinity, to the one of a diffusion process associated with the linear Landau equation. The proof of the convergence of the martingale problem relies on two key ingredients: long time stability results of the microscopic dynamics, and controls on the probability of particle recollisions. |
| title | Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2602.16440 |