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

## TL;DR

This paper rigorously derives the linear Landau equation from a particle system with short-range interactions in a weak-coupling regime, bridging microscopic dynamics and kinetic equations.

## Contribution

It provides a rigorous derivation of the linear Landau equation from particle interactions, connecting Boltzmann and Landau equations in a novel weak-coupling setting.

## Key findings

- Asymptotic equivalence between one-particle marginal and linear Boltzmann solution
- Derivation of Landau equation via grazing collision limit
- Validation of kinetic equations from particle systems

## Abstract

We consider a system of N particles interacting via a short-range smooth potential, in a intermediate regime between the weak-coupling and the low-density. 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.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.