  The dynamical friction and diffusion coefficients are derived for a massive
binary that moves against a uniform background of stars. The random impulses
exerted on the binary's center of mass by the field stars are greater than
those exerted on a point particle due to inelastic scattering. The frictional
force acting on the binary is less than that acting on a point particle due to
randomization of the trajectories of field stars that pass near the binary.
Both effects tend to increase the random motion of a binary compared with that
of a point mass. If the maximum effective impact parameter for gravitational
encounters is comparable to the radius of gravitational influence of the
binary, its Brownian velocity can be increased by a modest factor compared with
that of a single particle. This condition is probably fulfilled in the case of
binary supermassive black holes in galactic nuclei.
