Lévy Flight & Superdiffusion — Cauchy/Stable Distributions

PARAMETERS

STATISTICS

Steps taken: 0
⟨r²⟩:
MSD exponent β:
Max jump:
Regime:

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)