  AGN disks have been proposed as promising locations for the mergers of
stellar mass black hole binaries (BBHs). Much recent work has been done on this
merger channel, but the majority focuses on stellar mass black holes (BHs)
orbiting in the prograde direction. Little work has been done to examine the
impact of retrograde orbiters (ROs) on the formation and mergers of BBHs in AGN
disks. Quantifying the retrograde contribution is important, since roughly half
of all orbiters should initially be on retrograde orbits when the disk forms.
We perform an analytic calculation of the evolution of ROs in an AGN disk.
Because this evolution could cause the orbits of ROs to cross those of prograde
BBHs, we derive the collision rate between a given RO and a given BBH orbiting
in the prograde direction. In the examples given here, ROs in the inner region
of the disk experience a rapid decrease in the semimajor axis of their orbits
while also becoming highly eccentric in less than a million years. This rapid
orbital evolution could lead to extreme mass ratio inspirals detectable by the
Laser Interferometer Space Antenna. The collision rates of our example ROs with
prograde BBHs in the migration trap depend strongly on the volume of the inner
radiation-pressure-dominated region which depends on the mass of the
supermassive black hole (SMBH). Rates are lowest for larger mass SMBHs, which
dominate the AGN merger channel, suggesting that merger rates for this channel
may not be significantly altered by ROs.
