  We study three point functions of half BPS operators in $\mathcal{N}=4$ super
Yang-Mills theory focusing on correltors of two of the operators with dimension
of order $\Delta\sim N^2$ and a light single trace operator. These describe
vacuum expectation values of type IIB supergravity modes in LLM backgrounds
that do not necessarily preserve the same symmetries as the background
solution. We propose a class of complex matrix models that fully capture the
combinatorics of the problem, and describe their solution in the large $N$
limit. In simple regimes when the dual description is in terms of widely
separated condensates of giant gravitons we find that the models are solvable
in the large $N$ and can be approximated by unitary Jacobi ensembles; we
describe how these distributions are reproduced in the dual bubbling geometry
picture for large droplets. In the case of two eigenvalue droplets the model is
exactly solvable at finite $N$. As a result we compute all half-BPS structure
constants of heavy-heavy-light type, and reproduce the formulas found via
holographic renormalization in the large $N$ limit. We also comment on
structure constants of three heavy operators.
