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Starting with some known localization (matrix model) representations forcorrelators involving 1/2 BPS circular Wilson loop $\cal W$ in ${\cal N}=4$ SYMtheory we work out their $1/N$ expansions in the limit of large 't Hooftcoupling $\lambda$. Motivated by a possibility of eventual matching to highergenus corrections in dual string theory we follow arXiv:2007.08512 and expressthe result in terms of the string coupling $g_{\rm s} \sim g^2_{\rm YM} \sim\lambda/N$ and string tension $T\sim \sqrt \lambda$. Keeping only the leadingin $1/T$ term at each order in $g_{\rm s} $ we observe that while the expansionof $\langle {\cal W} \rangle$ is a series in $g^2_{\rm s} /T$, the correlatorof the Wilson loop with chiral primary operators ${\cal O}_J $ has expansion inpowers of $g^2_{\rm s}/T^2$. Like in the case of $\langle {\cal W} \rangle$where these leading terms are known to resum into an exponential of a"one-handle" contribution $\sim g^2_{\rm s} /T$, the leading strong couplingterms in $\langle {\cal W}\, {\cal O}_J \rangle$ sum up to a simple square rootfunction of $g^2_{\rm s}/T^2$. Analogous expansions in powers of $g^2_{\rms}/T$ are found for correlators of several coincident Wilson loops and theyagain have a simple resummed form. We also find similar expansions forcorrelators of coincident 1/2 BPS Wilson loops in the ABJM theory.

On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators