THE WEAK COUPLING LIMIT OF DISORDERED COPOLYMER MODELS

• 成果类型: Article
• 署名作者: Caravenna, Francesco; Giacomin, Giambattista
• 署名单位: University of Padua; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP546
• 发表日期: 2010
• 页码: 2322-2378
• 关键词: localization transition; selective interfaces; polymer

摘要

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 non-homogeneous 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 [alpha is an element of (0, 1)] family of continuum models, based on a-stable regenerative sets.