Lévy Stable Random Walks
Heavy-tailed distributions, superdiffusion & the generalized central limit theorem
Lévy Parameters
Stability α:
1.5
(1=Cauchy, 2=Gaussian)
Skewness β:
0.0
Scale c:
1.0
Steps:
500
Walkers:
5
New Walk
Compare α
Max |step|
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MSD exponent
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Diffusion type
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Lévy stable:
Characteristic function φ(k) = exp(−c^α|k|^α(1+iβ sign(k) tan(πα/2))). For α < 2: power-law tails P(x) ~ |x|^(−1−α), infinite variance. MSD ~ t^(2/α) (superdiffusion). Generalized CLT: sum of i.i.d. heavy-tail r.v.s converges to Lévy stable, not Gaussian.