Limit Multiplicity For Unitary Groups and The Stable Trace Formula

We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic subgroups of unitary groups. The representations considered are transfers of products of characters and discrete series on endoscopic groups, and the bounds are obtained using Arthur’s stabilization of the trace formula and the endoscopic classification of representations due to Mok and Kaletha-Minguez-Shin-White.