Propagation of chaos for the Boltzmann equation with soft potentials

This talk deals with the derivation of the space homogeneous Boltzmann equation in dimension 3, from a Kac-like interacting particles system. The collision kernel is of the form $B(z,\cos(\theta)) =|z|^\gamma b(\cos(\theta))$ with $\sin(\theta)b(\cos(\theta))\sim \theta^{-1-\nu}$ for $\gamma\in (-2,0)$ and $\nu\in(0,2)$ satisfying $\gamma+\nu>0$. The result is obtained by a compacity argument, and the convergence result is given without rate, as in the work by Fournier and Hauray concerning the Landau equation.