The Burnett expansion of the periodic Lorentz gas

Recently, stretched exponential decay of multiple correlations in the periodic Lorentz gas has been used to show the convergence of a series of correlations which has the physical interpretation as the fourth order Burnett coefficient, a generalisation of the diffusion coefficient. Here the result is extended to include all higher order Burnett coefficients, and give a plausible argument that the expansion constructed from the Burnett coefficients has a finite radius of convergence.