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We consider a system of N particles interacting via a short-range smooth potential, in a weak-coupling regime. This means that the number of particles \begin{document}$N$\end{document} goes to infinity and the range of the potential \begin{document}$e$\end{document} goes to zero in such a way that \begin{document}$Ne^{2} = α$\end{document} , with \begin{document}$α$\end{document} diverging in a suitable way. We provide a rigorous derivation of the Linear Landau equation from this particle system. The strategy of the proof consists in showing the asymptotic equivalence between the one-particle marginal and the solution of the linear Boltzmann equation with vanishing mean free path. This point follows [ 3 ] and makes use of technicalities developed in [ 16 ]. Then, following the ideas of Landau, we prove the asympotic equivalence between the solutions of the Boltzmann and Landau linear equation in the grazing collision limit.

The rigorous derivation of the Linear Landau equation from a particle system in a weak-coupling limit