Journal of Statistical Physics, Vol. 100, Nos. 3/4, 2000. p. 603-632.
Using a compactness argument based on the velocity averaging lemma of Golse et al., it is shown that the limiting behavior of a kinetic (linearized BGK) gas model confined between two plates with Maxwell boundary conditions, when the distance between the plates goes to zero, under a suitable anomalous scaling, is diffusive. We do not require the use of central limit theorems as in the method of Borgers et al.