The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L1 senses.
Entropy-cost type Propagation of Chaos for Mean Field Particle System with Bounded Measurable Interaction
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In this paper, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is obtained, where the interaction is assumed to be bounded. More precisely, the relative entropy between the distributions of particle system and the corresponding McKean-Vlasov SDEs at any positive time $t$ depends on $L^1$-transportation cost $\W_1^\Psi$ between the initial distributions. The results weaken the initial assumptions in existing entropy-entropy type propagation of chaos.
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Kac's Program for the Landau Equation
The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L1 senses.