  With the aim to investigate the statistical properties and the connection
between thermal and non-thermal properties of the ICM in galaxy clusters, we
have developed a statistical magneto-turbulent model which describes, at the
same time, the evolution of the thermal and non-thermal emission from galaxy
clusters. In particular, starting from the cosmological evolution of clusters,
we follow cluster mergers, calculate the spectrum of the magnetosonic waves
generated in the ICM during these mergers, the evolution of relativistic
electrons and the resulting synchrotron and Inverse Compton spectra. We show
that the broad band (radio and hard x-ray) non-thermal spectral properties of
galaxy clusters can be well accounted for by our model for viable values of the
parameters.
