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We present dielectric spectroscopy data obtained for gallium-dopedCd$_{0.99}$Mn$_{0.01}$Te:Ga mixed crystals which exhibit a very special case ofthe two-power-law relaxation pattern with the high-frequency power-law exponentequal to 1. We explain this behavior, which cannot be fitted by none of thewell-known empirical relaxation functions, in a subordinated diffusiveframework. We propose diffusion scenario based on a renormalized clustering ofrandom number of spatio-temporal steps in the continuous time random walk. Sucha construction substitutes the renewal counting process, used in the classicalcontinuous time random walk methodology, by a compound counting one. As aresult, we obtain a novel relaxation function governing the observednon-standard pattern, and we show the importance of the compound countingprocesses in studying fractional dynamics of complex systems.

Experimental Evidence of the Role of Compound Counting Processes in Random Walk Approaches to Fractional Dynamics