The Boltzmann-Grad limit for a one-dimensional Boltzmann equation in a stationary state

In this paper we consider a one-dimensional model of interacting particles in a bounded interval with (possibly not homogeneous) diffusive boundary conditions. We prove that, when the number of particlesN goes to infinity and the interaction is suitably rescaled (the Boltzmann-Grad limit), the one-particle distribution function of the unique invariant measure for the particle system, converges to the unique solution of the Boltzmann equation of the model, provided that the mean free path is sufficiently large.