Study of protected BPS operators in N=4 SYM via complex matrix models

We propose and study a family of complex matrix models computing the protected two- and three-point correlation functions in $\mathcal{N}=4$ SYM. Our description allows us to directly relate the eigenvalue density of the matrix model for "Huge" operators with $ \Delta \sim N^2$ to the shape of droplets in the dual Lin-Lunin-Maldacena (LLM) geometry. We show how this description allows to calculate various three-point functions involving huge operators. The talk is based on arXiv:2508.20094