We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity δ∈ℝ of the pinning interaction is constant, while the interface spacing T=TN is allowed to vary with the size N of the polymer. Our main result is the explicit determination of the scaling behavior of the model in the large N limit, as a function of (TN)N and for fixed δ>0. In particular, we show that a transition occurs at TN=O(log N). Our approach is based on renewal theory.
"A polymer in a multi-interface medium." Ann. Appl. Probab. 19 (5) 1803 - 1839, October 2009. https://doi.org/10.1214/08-AAP594