We show how to modify the random-walk scenario underlying the classical, exponential relaxation response in order to derive the empirical Havriliak--Negami function, commonly used to fit the dielectric permittivity of complex-material 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 continuous-time random walk (CTRW) driving a fractional dynamics.

PACS numbers: 77.22.Gm, 02.50.--r, 05.40.Fb