Central limit theorem for the Lorentz process via perturbation theory

The Markov partition of the Sinai billiard allows the following heuristic interpretation for the Lorentz process with a ²-periodic configuration of scatterers: while executing a (non-Markovian) random walk on ², and particle changes its internal state according to the symbolic dynamics defined by the Markov partition. This picture can be formalized and then the Lorentz process appears as the limit of a sequence of (Markovian!) random walks with a finite but increasing number of internal states and the central limit theorem can be proved for it by perturbational expansions with uniformly bounded — in a sence related to the Perron-Frobenius theorem — coefficients and uniform remainder terms.