We calculate the probability to form giant radio halos (~ 1 Mpc size) as a
function of the mass of the host clusters by using a Statistical
Magneto-Turbulent Model (Cassano & Brunetti, these proceedings). We show that
the expectations of this model are in good agreement with the observations for
viable values of the parameters. In particular, the abrupt increase of the
probability to find radio halos in the more massive galaxy clusters (M >
2x10^{15} solar masses) can be well reproduced. We calculate the evolution with
redshift of such a probability and find that giant radio halos can be powered
by particle acceleration due to MHD turbulence up to z~0.5 in a LCDM cosmology.
Finally, we calculate the expected Luminosity Functions of radio halos (RHLFs).
At variance with previous studies, the shape of our RHLFs is characterized by
the presence of a cut-off at low synchrotron powers which reflects the
inefficiency of particle acceleration in the case of less massive galaxy
clusters.Comment: 4 pages, to appear in a dedicated issue of the Journal of the Korean
Astronomical Society (JKAS). Proceedings of the "International conference on
Cosmic Rays and Magnetic Fields in Large Scale Structure", Busan, Korea, 200
