A probabilistic result on the disordered pinning model, a random polymer defined by a Gibbs transform of a renewal process, when the random environment is Gaussian with long-range, power-law correlations set by a Hurst parameter. In the disorder-relevant regime, the paper analyzes the intermediate-disorder scaling and proves that the suitably rescaled partition functions converge weakly to a nontrivial continuum limit represented by a Wiener-chaos expansion, established in both the Skorohod and Stratonovich stochastic-integration settings, partially confirming the Weinrib-Halperin disorder-relevance prediction.
The disordered pinning model is a random-polymer model built by a Gibbs reweighting of a renewal process using a random environment (the disorder). This paper treats disorder that is Gaussian and lon…