  We consider point particle that collides with a periodic array of hard-core
elastic scatterers where the length of the free flights is unbounded (the
infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT)
states that the distribution of the particle displacement divided by
$\sqrt{t\ln t}$ is Gaussian in the limit of infinite time $t$. However it was
stressed recently that the slow convergence makes this result unobservable.
Using a L\'{e}vy walk model (LW) of the LG, it was proposed that the use of a
rescaled Lambert function instead of $\sqrt{t\ln t}$ provides a fast
convergent, observable CLT, which was confirmed by the LG simulations. We
demonstrate here that this result can simplified to a mixed CLT where the
scaling factor combines normal and anomalous diffusions. For narrow infinite
corridors the particle for long time obeys the usual normal diffusion, which
explains the previous numerical observations. In the opposite limit of small
scatterers the Bleher CLT gives a good guiding. In the intermediate cases the
mixed CLT applies. The Gaussian peak determines moments of order smaller than
two. In contrast, the CLT gives only half the coordinate dispersion. The
missing half of the dispersion and also moments of order higher than two are
described by the distribution's tail (the infinite density) which we derive
here. The tail is supported along the infinite corridors and formed by
anomalously long flights whose duration is comparable with the whole time of
observation. The moments' calculation from the tail is confirmed by direct
calculation of the fourth moment from the statistics of the backward recurrence
time defined as time that elapsed since the last collision. This completes the
solution of the LW model allowing full comparison with the LG.
