  Quantum black holes are difficult to describe. We consider two seemingly
divergent approaches, high-energy scattering and the proposal to regard black
holes as Bose-Einstein condensates of gravitons, and establish a connection
between them. High-energy scattering is studied in the eikonal approximation,
which is processed further by a saddle-point approximation. The dominant
contribution to the scattering amplitude comes from a ladder diagram with the
exchange of N gravitons, and the number of gravitons follows a Poisson
distribution. This approximation supports the picture of a graviton
Bose-Einstein condensate with an extent equal the Schwarzschild radius, which
grows with N in a way determined by the saddle point. The approach permits
calculations of 1 / N corrections from the fluctuations around the saddle
points and we comment on these. Scattering methods might be useful probes of
quantum black holes, especially when interpreted in terms of condensates.
