Scaling limits and stochastic homogenization for some nonlinear parabolic equations

The aim of this paper is twofold. first to study the asymptotics a parabolically scaled, continuous and space-time stationary in time version well-known Funaki-Spohn model Statistical Physics. After change unknowns requiring existence eternal solution stochastically perturbed heat equation, problem transforms qualitative homogenization uniformly elliptic, stationary, divergence form, nonlinear partial differential which second paper. An important step construction correctors with appropriate behavior at infinity.