Pin a tail on the distribution?

• What sort of stochastic processes generate tails?

  • For the sake of transparency, we will discuss spatial distributions that depart from Gaussian, and later apply these distributions to velocity space Maxwellians.
  • If we consider a random stochastic process, such as a drunk staggering around a lamppost, we can plot the resulting spatial distribution of a collection of drunks.
  • For some simple restrictions, the Central Limit Theorem predicts the distribution will converge to a Gaussian.
  • Even worse, the distribution that maximizes entropy while conserving energy is a Maxwellian= Gaussian in v-space.

• How can we get a tail without violating the physics?