Lévy Stable Distributions & α-Stable Processes
Generalized CLT: stable laws, fat tails, superdiffusion
Parameters
Stability α:
1.50
(α=2: Gaussian)
Skewness β:
0.00
Scale γ:
1.0
N walkers:
200
Reset Walkers
New Sample
Theory
φ(t) = exp(iμt - γ|t|^α(1+iβsgn(t)Φ))
α=2: Gaussian (finite variance)
α<2: power tail P(X>x)~x^(-α)
MSD: ⟨x²(t)⟩ ~ t^(2/α) (superdiff)
Statistics