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 T N = O(log N). Our approach is based on renewal theory. © Institute of Mathematical Statistics, 2009.
Caravenna, F., Petrelis, N. (2009). A polymer in a multi-interface medium. THE ANNALS OF APPLIED PROBABILITY, 19(5), 1803-1839 [10.1214/08-AAP594].
A polymer in a multi-interface medium
CARAVENNA, FRANCESCO;
2009
Abstract
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 T N = O(log N). Our approach is based on renewal theory. © Institute of Mathematical Statistics, 2009.
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