A simple stochastic mechanism that produces exact and approximate
power-law distributions is presented. The model considers radially symmetric
Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a
radially uniform sampling scheme produces heavy-tailed distributions. For
two-dimensional Gaussians and one-dimensional exponential functions, exact
power-laws with exponent
–1 are obtained. In other cases, densities with an
approximate power-law behaviour close to the origin arise. These densities are
analyzed using Padé approximants in order to show the approximate power-law behaviour.
If the sampled function itself follows a power-law with exponent
–α, random sampling leads to densities
that also follow an exact power-law, with exponent -n/a
– 1. The presented mechanism shows that power-laws can arise in generic
situations different from previously considered specialized systems such as
multi-particle systems close to phase transitions, dynamical systems at
bifurcation points or systems displaying self-organized criticality. Thus, the
presented mechanism may serve as an alternative hypothesis in system
identification problems.