  We study the two-point correlator of an O(N) scalar field with quartic
self-coupling in de Sitter space. For light fields in units of the expansion
rate, perturbation theory is plagued by large logarithmic terms for
superhorizon momenta. We show that a proper treatment of the infinite series of
self-energy insertions through the Schwinger-Dyson equations resums these
infrared logarithms into well defined power laws. We provide an exact
analytical solution of the Schwinger-Dyson equations for infrared momenta when
the self-energy is computed at two-loop order. The obtained correlator exhibits
a rich structure with a superposition of free-field-like power laws. We extract
mass and field-strength renormalization factors from the asymptotic infrared
behavior. The latter are nonperturbative in the coupling in the case of a
vanishing tree-level mass.
