Displacement autocorrelation functions for strong anomalous diffusion: A scaling form, universal behavior, and corrections to scaling

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments displacement, with exponents that do not depend linearly on order moment. The concerning small-order are dominated random motion, while higher-order grow faster trajectories, such as ballistic excursions or "light fronts". Often a situation two linear dependencies their order. Here, we introduce simple exactly solvable model, Fly-and-Die (FnD) sheds light this behavior and consequences fronts displacement autocorrelation functions in transport processes. We present analytical expressions for derive scaling form expresses long-time asymptotics function $\langle x(t_1)\,x(t_2)\rangle$ terms dimensionless time difference $(t_2-t_1)/t_1$. provides faithful collapse numerical data vastly different systems. This demonstrated here Lorentz gas infinite horizon, polygonal billiards finite L\'evy-Lorentz gas, Slicer Map, L\'evy walks. Our analysis also captures system-specific corrections to scaling.