Diffusive limit for the random Lorentz Gas

We review some recent results concerning the derivation of the diffusion equation and the validation of Fick’s law for the microscopic model given by the random Lorentz Gas. These results are achieved by using a linear kinetic equation as an intermediate level of description between our original mechanical system and the diffusion equation. The diffusion coefficient is given by the Green-Kubo formula associated to the generator of the stochastic process dictated by the linear Landau equation and the linear Boltzmann equation respectively, according to the weak coupling regime and low density regime we are considering.