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November 2010 The weak coupling limit of disordered copolymer models
Francesco Caravenna, Giambattista Giacomin
Ann. Probab. 38(6): 2322-2378 (November 2010). DOI: 10.1214/10-AOP546


A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a nonhomogeneous medium, for example, made of two solvents separated by an interface. One may observe, for instance, the localization of the polymer at the interface between the two solvents. A discrete model of such system, based on the simple symmetric random walk on ℤ, has been investigated in [8], notably in the weak polymer-solvent coupling limit, where the convergence of the discrete model toward a continuum model, based on Brownian motion, has been established. This result is remarkable because it strongly suggests a universal feature of copolymer models. In this work, we prove that this is indeed the case. More precisely, we determine the weak coupling limit for a general class of discrete copolymer models, obtaining as limits a one-parameter [α ∈ (0, 1)] family of continuum models, based on α-stable regenerative sets.


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Francesco Caravenna. Giambattista Giacomin. "The weak coupling limit of disordered copolymer models." Ann. Probab. 38 (6) 2322 - 2378, November 2010.


Published: November 2010
First available in Project Euclid: 24 September 2010

zbMATH: 1242.82022
MathSciNet: MR2683632
Digital Object Identifier: 10.1214/10-AOP546

Primary: 60K05 , 60K37 , 82B41 , 82B44

Keywords: Coarse-graining , Copolymer , phase transition , Regenerative set , Renewal process , Universality , weak coupling limit

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 6 • November 2010
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