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Many stellar-mass Black Holes (sBHs) are expected to orbit supermassive blackholes at galactic centers. For galaxies with Active Galactic Nuclei (AGN), itis likely that the sBHs reside in a disk. We study the formation of sBHbinaries via gravitational wave emission in such disks. We examine analyticallythe dynamics of two sBHs orbiting a supermassive black hole, estimate thecapture cross-section, and derive the eccentricity distribution of boundbinaries at different frequency bands. Thus, we estimate that $\sim 50\%$ ofthe merging stellar-mass black hole binaries, assembled in this manner, havehigh eccentricities, $e\gtrsim0.5$, in the LIGO-Virgo-KAGRA band. Aconsiderable fraction of these mergers leads to a direct plunge rather than aneccentric inspiral. More eccentric mergers would be observed for sBHs withhigher random velocities, closer to the supermassive black hole, or at lowerobserving frequency bands, as planned in future gravitational wave detectorssuch as the Einstein Telescope and LISA.

Formation of Merging Stellar-Mass Black Hole Binaries by Gravitational Waves Emission in AGN Disks