Journal of Statistical Physics, Vol. 79, Nos. 5/6, 1995. p. 993-1003.
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 power-law coefficients n and m is the necessary and sufficient condition to obtain the low- and high-frequency power-law behavior. Consequently, in both frequency regions the Kramers-Kr6nig-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 stochastic considerations does cover the full range of the observed dielectric responses.