par Le Bihan, Corentin 
Référence Communications on pure and applied mathematics, 79, 7, page (1673-1745)
Publication Publié, 2026-02-26
Référence Communications on pure and applied mathematics, 79, 7, page (1673-1745)
Publication Publié, 2026-02-26
Article révisé par les pairs
| Résumé : | ABSTRACT We provide a rigorous justification of the linearized Boltzmann and Landau equations for interacting particle systems with long‐range interaction. The result shows that for a system of Hamiltonian particles governed by truncated power law potentials of the form near (with the effective radius of the particles), the covariance of the equilibrium fluctuations converges to solutions of kinetic equations in appropriate scaling limits and , corresponding to a low density regime. We prove that in Dimension 3, for , the limiting system approaches the uncut‐off linearized Boltzmann equation for the scaling . The Coulomb singularity appears as a threshold value. Kinetic scaling limits with universally converge to the linearized Landau equation, and we prove the onset of the Coulomb logarithm for . |
