Superdiffusion, subdiffusion, and non-ergodic aging in stochastic processes
Lévy walks (α < 2) produce superdiffusion: ⟨x²⟩ ~ t^γ with γ > 1. Continuous-time random walks (CTRW) with heavy-tailed waiting times produce subdiffusion (γ < 1). Both are anomalous: normal diffusion gives γ = 1. Aging occurs when the MSD depends on the observation start time — a signature of non-ergodicity fundamental to glasses and biological motion.