Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics.

We present dielectric spectroscopy data obtained for gallium-doped Cd(0.99)Mn(0.01)Te:Ga mixed crystals, which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by any of the well-known empirical relaxation functions, in a subordinated diffusive framework. We propose a diffusion scenario based on a renormalized clustering of a random number of spatio-temporal steps in the continuous-time random walk. Such a construction substitutes the renewal counting process, which is used in the classical continuous time random walk methodology, with a compound counting one. As a result, we obtain an appropriate relaxation function governing the observed nonstandard pattern, and we show the importance of the compound counting processes in studying fractional dynamics of complex systems.