Immediately following the formation of a hard black-hole binary, the density cusp of the merged galaxies is nearly homologous to the cusps in the initial galaxies. When the distance between the black holes becomes comparable to the average stellar separation in the cusp, the binary begins to wander about the center while engaging in hard encounters with stars on radial orbits that are ejected at high speed.
Ejection induces further shrinking of the binary at a decreasing rate.
We discuss the dynamics of black hole binaries in the limit of large N, appropriate to real galactic nuclei, and discuss the possibility that supermassive black hole binaries can survive over cosmological times. This link was provided by the author.