On a pinning model in correlated Gaussian random environments

TL;DR

This paper investigates a pinning model in correlated Gaussian environments, analyzing its intermediate disorder regime and demonstrating convergence of rescaled partition functions to continuum limits, thus providing insights into disorder relevance predictions.

Contribution

It introduces a detailed analysis of the intermediate disorder regime for correlated Gaussian pinning models and confirms parts of the Weinrib--Halperin disorder relevance prediction.

Findings

Rescaled partition functions converge to non-trivial limits in Skorohod and Stratonovich settings.

Results support the Weinrib--Halperin prediction on disorder relevance.

Partial confirmation of theoretical predictions for correlated Gaussian environments.

Abstract

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.