Brownian dynamics around the core of self-gravitating systems
  We derive the non-Maxwellian distribution of self-gravitating $N$-body
systems around the core by a model based on the random process with the
additive and the multiplicative noise. The number density can be obtained
through the steady state solution of the Fokker-Planck equation corresponding
to the random process. We exhibit that the number density becomes equal to that
of the King model around the core by adjusting the friction coefficient and the
intensity of the multiplicative noise. We also show that our model can be
applied in the system which has a heavier particle. Moreover, we confirm the
validity of our model by comparing with our numerical simulation.
