  Intermediate-mass black holes (IMBHs) are believed to be the missing link
between the supermassive black holes (BHs) found at the centers of massive
galaxies and BHs formed through stellar core collapse. One of the proposed
mechanisms for their formation is a collisional runaway process in high-density
young star clusters, where an unusually massive object forms through repeated
stellar collisions and mergers, eventually collapsing to form an IMBH. This
seed IMBH could then grow further through binary mergers with other
stellar-mass BHs. Here we investigate the gravitational-wave (GW) signals
produced during these later IMBH--BH mergers. We use a state-of-the-art
semi-analytic approach to study the stellar dynamics and to characterize the
rates and properties of IMBH--BH mergers. We also study the prospects for
detection of these mergers by current and future GW observatories, both
space-based (LISA) and ground-based (LIGO Voyager, Einstein Telescope, and
Cosmic Explorer). We find that most of the merger signals could be detected,
with some of them being multi-band sources. Therefore, GWs represent a unique
tool to test the collisional runaway scenario and to constrain the population
of dynamically assembled IMBHs.
