LÉVY THEORY
P(x) ~ |x|^{-(1+α)}, 0<α<2
Superdiffusion: ⟨r²⟩ ~ t^{2/α}
α<1: ballistic-like
α=1: Cauchy, ⟨r²⟩ diverges
α=2: Gaussian (Brownian)
Generalized CLT → stable distributions
Lévy-Khintchine theorem
Characteristic function:
φ(k) = exp(−σ^α|k|^α)
Lévy exponent: ν = 2/α (α<2)