The damped wave equation and associated polymer

Abstract

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 will see that this equation has a mild solution which is stationary in time $t$. We define a weakly self-avoiding polymer with intrinsic length $J$ associated to this SPDE. Our main result is that the polymer has an effective radius of approximately $J^{5/3}$.