A Note on Gravitational Brownian Motion
  Chandrasekhar's theory of stellar encounters predicts a dependence of the Brownian motion of a massive particle on the velocity distribution of the perturbing stars. One consequence is that the expectation value of the massive object's kinetic energy can be different from that of the perturbers. This effect is shown to be modest however, and substantially smaller than claimed in a recent study based on a more approximate treatment of the encounter equations. 
David Merritt