Trajectory (orange=Lévy, blue=Brownian)
Lévy Walk Physics:
A Lévy walk draws step lengths from P(ℓ) ~ ℓ^{−μ} (power-law, heavy tails). For 1<μ<3: superdiffusive MSD⟨r²⟩ ~ t^α with α = (4−μ)/(μ−1) for Lévy walks (velocity model). At μ=2: α≈2 (ballistic-like). At μ→3: α→1 (normal diffusion recovered). The key insight: rare long jumps ("Lévy flights") dominate the spread. Found in animal foraging (albatross, sharks), light scattering in hot atomic vapors (Lévy glasses), human mobility, and financial returns. Distinct from Lévy flights (instantaneous jumps) — walks have finite velocity.