Anomalous diffusion: subdiffusion (α<1) and superdiffusion (α>1)
Wait-time exponent α0.70
Jump exponent β2.00
Walkers5
Speed2.0
Normal (α=β=2)CTRW walkersMSD slope
CTRW: random walk with waiting times drawn from power-law distribution ψ(t) ~ t^(-1-α). For α<1, the mean waiting time is infinite → subdiffusion: MSD ~ t^α. Jump lengths from Lévy distribution (exponent β<2) → superdiffusion: MSD ~ t^(2/β) for β<2. Combined: MSD ~ t^(α·min(2,2/β)). The fractional diffusion equation ∂^α p/∂t^α = K_α ∇² p has CTRW as its mesoscopic limit (Metzler & Klafter 2000).