  The recently discovered gravitational wave sources GW190521 and GW190814 have
shown evidence of BH mergers with masses and spins that could be outside of the
range expected from isolated stellar evolution. These merging objects could
have undergone previous mergers. Such hierarchical mergers are predicted to be
frequent in active galactic nuclei (AGN) disks, where binaries form and evolve
efficiently by dynamical interactions and gaseous dissipation. Here we compare
the properties of these observed events to the theoretical models of mergers in
AGN disks, which are obtained by performing one-dimensional $N$-body
simulations combined with semi-analytical prescriptions. The high BH masses in
GW190521 are consistent with mergers of high-generation (high-g) BHs where the
initial progenitor stars had high metallicity, 2g BHs if the original
progenitors were metal-poor, or 1g BHs that had gained mass via super-Eddington
accretion. Other measured properties related to spin parameters in GW190521 are
also consistent with mergers in AGN disks. Furthermore, mergers in the lower
mass gap or those with low mass ratio as found in GW190814 and GW190412 are
also reproduced by mergers of 2g-1g or 1g-1g objects with significant accretion
in AGN disks. Finally, due to gas accretion, the massive neutron star merger
reported in GW190425 can be produced in an AGN disk.
