The stellar ejection rate and the rates of change of the binary semimajor axis and eccentricity are derived from scattering experiments for the restricted three-body problem. They are used to study the evolution of binaries in simple models for galactic nuclei, starting soon after the black holes become bound and continuing until the evolution is dominated by the emission of gravitational radia...

We introduce notions of certificates allowing to bound eccentricities in a graph. In particular, we revisit radius (minimum eccentricity) and diameter (maximum eccentricity) computation and explain the efficiency of practical radius and diameter algorithms by the existence of small certificates for radius and diameter plus few additional properties. We show how such computation is related to co...