Lévy stable distribution: step lengths ℓ follow P(ℓ) ~ ℓ^{−(α+1)} for large ℓ, with 1 < α < 2. The variance diverges — these are heavy-tailed jumps. Anomalous diffusion: ⟨r²(t)⟩ ~ t^{2/α} for 1 < α < 2 (superdiffusion; normal diffusion gives t^1). As α→2, approaches Gaussian/Brownian; as α→1, approaches Cauchy with infinite mean. Lévy search: for sparse targets, Lévy flights minimize expected search time — many short local searches punctuated by rare long jumps is optimal (Viswanathan et al., Nature 1999).