Random Walk & Lévy Flight
Brownian motion vs. Lévy flight: fat tails and superdiffusion
Brownian Motion (Gaussian steps)
Lévy Flight (Power-law steps)
Parameters
Lévy index α:
1.5
Walkers:
5
Trail length:
200
Speed:
3
x
Reset Walkers
Statistics
Brownian MSD
0
Lévy MSD
∞
Steps taken
0
α regime
super
α < 1: Cauchy-like, superdiffusion
α = 2: recovers Brownian motion
MSD ~ t^(2/α) for Lévy (if α < 2)
Variance
diverges
for α < 2