Frequency-independent rules for the dielectric susceptibility derived from two forms of self-similar dynamical behavior of dipolar systems

This paper provides the frequency domain analysis of the probabilistic representation of the cluster model for dielectric relaxation in dipolar systems. It is proved that the restriction (0.1) experimentally found for both the powerlaw coefficientsn andm is the necassary and sufficient condition to obtain the low- and high-frequency power-law behavior. Consequently, in both frequency regions the Kramers-Krönig-compatible frequency-independent rules are fulfilled. Moreover, in contrast to the empirical functions proposed to fit the experimental data, the dielectric susceptibility derived from the stochastioc considerations does cover the full range of the observed dielectric responses.