  By considering a Gaussian truncation of ${\cal N}=4$ super Yang-Mills, we
derive a set of Dyson equations that account for the ladder diagram
contribution to connected correlators of circular Wilson loops. We consider
different numbers of loops, with different relative orientations. We show that
the Dyson equations admit a spectral representation in terms of eigenfunctions
of a Schr\"odinger problem, whose classical limit describes the strong coupling
limit of the ladder resummation. We also verify that in supersymmetric cases
the exact solution to the Dyson equations reproduces known matrix model
results.
