Lévy stable distributions S(α,β,c,μ) generalize the Gaussian (α=2). For α < 2, tails decay as |x|^(−1−α) — power laws, not exponentials. The characteristic function is φ(t) = exp(iμt − c^α|t|^α(1−iβ sgn(t) tan(πα/2))). Sum of N i.i.d. Lévy variables → heavy tails persist.