  The large $N$ expansion of giant graviton correlators is considered. Giant
gravitons are described using operators with a bare dimension of order $N$. In
this case the usual $1/N$ expansion is not applicable and there are
contributions to the correlator that are non-perturbative in character. By
writing the (square of the) correlators in terms of the hypergeometric function
${}_2F_1(a,b;c;1)$, we are able to rephrase the $1/N$ expansion of the
correlator as a semi-classical expansion for a Schr\"odinger equation. In this
way we are able to argue that the $1/N$ expansion of the correlator is Borel
summable and that it exhibits a parametric Stokes phenomenon as the angular
momentum of the giant graviton is varied.
