This paper presents a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent $\alpha \in (0,1/2)$. We also give a new upper bound for the contact fraction of the disordered model at criticality.
Hubert Lacoin. "The Martingale approach to disorder irrelevance for pinning models." Electron. Commun. Probab. 15 418 - 427, 2010. https://doi.org/10.1214/ECP.v15-1572