Scaling properties of the diffusion process underlying the Havriliak-Negami relaxation function

We present a generalization of the exponential Debye relaxation based on the continuous-time random walk (CTRW) framework. We show how to modify the random-walk scenario underlying the classical response in order to derive the empirical Havriliak-Negami function, commonly used to fit the experimental relaxation data. The turnover from the exponential Debye to the power-law Havriliak-Negami relaxation response is associated with a new type of a coupled memory CTRW driving a fractional dynamics.