Invariance principle for the periodic Lorentz gas in the Boltzmann-Grad limit
arXiv:1506.03619
Abstract
In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present paper extends this result to a functional central limit theorem, i.e., the weak convergence of the particle trajectory to Brownian motion.
This paper has been merged with arXiv:1403.6024; to appear in Communications in Mathematical Physics