On the Smoluchowski-Kramers approximation for the hyperbolic $O(N)$ linear sigma model and its mean-field limit

Alexander Czernik, Ruoyuan Liu, Shao Liu

We study the hyperbolic $O(N)$ linear sigma model, i.e. a system of $N$ interacting stochastic damped nonlinear wave equations (SdNLW) with coupled cubic nonlinearities, posed on t…