On a pinning model in correlated Gaussian random environments

We consider a pinning model in correlated Gaussian random environments. For the model that is disorder relevant, we study its intermediate disorder regime and show that the rescaled partition functions converge to a non-trivial continuum limit in the Skorohod setting and in the Stratonovich setting, respectively. Our results partially confirm the Weinrib–Halperin prediction for disorder relevance/irrelevance.