Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas

Thierry Bodineau; Pierre Le Bris

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arXiv · 2602.16440

Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas

Thierry Bodineau·Pierre Le Bris

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Abstract

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.

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Thierry Bodineau, Pierre Le Bris. 2026-02-18. Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas. https://arxiv.org/abs/2602.16440

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