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Linear Landau equation as a limit of a tagged particle in mean field interaction with a free gas
Thierry Bodineau, Pierre Le Bris · 2026-02-18 · via math.PR updates on arXiv.org

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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