Journal of Statistical Physics, Vol. 70, Nos. 3/4, 1993. p. 793-809.
The probability of first return to the initial interval x and the diffusion tensor are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution...