Brownian motion of supermassive black holes in galaxy cores
  We investigate the dynamics of supermassive black holes (SMBHs) in galactic
cores by means of a semi-analytic model based on the Langevin equation,
including dynamical friction and stochastic noise accounting for the
gravitational interactions with stars. The model is validated against direct
$N$-body simulations of intermediate-mass black holes in stellar clusters where
a realistic number of particles is accessible. For the galactic case, we find
that the SMBH experiences a Brownian-like motion with a typical displacement
from the geometric center of the Galaxy of a few parsecs, for system parameters
compatible with M87. \keywords{stellar dynamics, black hole physics, methods:
n-body simulations, methods: statistical.
