  We revisit effective scenarios for the origin of heavy tails in stationary
velocity distributions. A first analysis combines localization with diffusive
acceleration. That gets realized in space plasmas to find the so-called
kappa-distributions having power-law decay at high speeds. There, localization
at high energy already takes place for the reversible dynamics but becomes
effective by an active diffusion in velocity space. A model for vibrating
granular gases and giving rise to stretched exponential tails is also briefly
discussed, where negative friction is the energizer. In all cases, the
resulting nonMaxwellian velocity distributions are frenetically caused by the
dependence on the speed of kinetic parameters.
