Stochastic Partial Differential Equations (SPDEs) represent a powerful and versatile mathematical framework that unifies two fundamental branches of mathematics: stochastic processes and partial differential equations. My works focus on the damped wave equation and Anderson models. Past works are: (1) Considering the damped wave equation with a Gaussian noise F where F is white in time and has a covariance function depending on spatial variables, we define a weakly self-avoiding polymer with intrinsic length J associated to this SPDE. The main result is that the polymer has an effective radius of approximately J^{5/3}. (2) Considering the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain D ⊂R^2. We compute the small time asymptotics  of the AH’s exponential trace up to order O(log t), and of the PAM’s mass up to order O(t log t).