We study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well- known Funaki-Spohn model in Statistical Physics. After a change of unknowns requiring the existence of a space-time stationary eternal solution of a stochastically perturbed heat equation, the problem transforms to the qualitative homogenization of a uniformly elliptic, space-time stationary, divergence form, nonlinear partial differential equation. An important step is the construction of correctors with the appropriate behavior at infinity.
This is joint work with P. Cardaliaguet and P.E. Souganidis