  We introduce the concept of multi-point propagators between linear cosmic
fields and their nonlinear counterparts in the context of cosmological
perturbation theory. Such functions express how a non-linearly evolved Fourier
mode depends on the full ensemble of modes in the initial density field. We
identify and resum the dominant diagrams in the large-$k$ limit, showing
explicitly that multi-point propagators decay into the nonlinear regime at the
same rate as the two-point propagator. These analytic results generalize the
large-$k$ limit behavior of the two-point propagator to arbitrary order. We
measure the three-point propagator as a function of triangle shape in numerical
simulations and confirm the results of our high-$k$ resummation. We show that
any $n-$point spectrum can be reconstructed from multi-point propagators, which
leads to a physical connection between nonlinear corrections to the power
spectrum at small scales and higher-order correlations at large scales. As a
first application of these results, we calculate the reduced bispectrum at
one-loop in renormalized perturbation theory and show that we can predict the
decrease in its dependence on triangle shape at redshift zero, when standard
perturbation theory is least successful.
