On the origin of power law distribution functions

Power law distribution functions of various properties are prevalent in a vast range of systems, from the smallest dust grains between stars to the largest dark matter halos. Power laws describes the frequency of various phenomena, and appears also in biology, economy, sociology, and linguistics. I will show simulations of a very simple system of colliding hard spheres, and use it to explore the general conditions where a power law distribution function appears, and the possible implications for various other systems.