Heavy-tailed random walks: the mathematics of foraging and wandering
Levy flight uses step lengths drawn from a power-law: P(l) ~ l^(-alpha). For alpha less than 2, variance is infinite
so occasional enormous jumps dominate the path. Found in albatross foraging, shark hunting, human travel, and financial markets.
Near alpha=2 it approaches Brownian motion; near alpha=1 jumps are maximally wild. The Levy exponent determines the fractal dimension.