I am following Hong Liu's MIT 8.821 String Theory and Holographic Duality lectures. He starts discussing the large-$N$ expansion in the context of a hermitian matrix model described by the Lagrangian
$$\mathcal{L}=-\frac{1}{g^2}\text{Tr} \left\{\frac{1}{2}\partial_\mu\Phi\partial^\mu\Phi+\frac{1}{4}\Phi^4\right\},$$
where $g$ is the coupling constant and $\Phi$ is a $N\times N$ hermitian matrix. He shows that the large-$N$ limit of this model only makes sense when we consider the 't Hooft parameter
$$\lambda_\text{'t Hooft}=g^2N,$$
and take the $N\rightarrow\infty$ limit while keeping $\lambda_\text{'t Hooft}$ fixed.
At some point in the lecture, a student asks a question regarding whether $\lambda_\text{'t Hooft}$ should be a small parameter or not, and Liu remarks that it does not matter, and later on in the course he will eventually take the limit $\lambda_\text{'t Hooft}\rightarrow\infty$.
My question is what is the point in considering the limit $\lambda_\text{'t Hooft}\rightarrow\infty$? What does it mean physically? Is it regarding some sort of a weak-strong coupling duality?
