Power-law jump lengths produce superdiffusion and heavy-tailed displacements
Steps: 0 | ⟨|x|⟩ = — | MSD ~ t^(2/α)
Lévy stable distributions S(α, β, c, μ) generalize the Gaussian (α=2) to heavy-tailed cases. For α<2, variance diverges and rare "Lévy flights" — large jumps — dominate. The mean-squared displacement grows as ⟨x²⟩ ~ t^(2/α) for α<2 (superdiffusion), versus linearly for Gaussian (α=2). Observed in animal foraging, turbulent diffusion, and financial markets.