Translator Disclaimer
August 2007 A renewal theory approach to periodic copolymers with adsorption
Francesco Caravenna, Giambattista Giacomin, Lorenzo Zambotti
Ann. Appl. Probab. 17(4): 1362-1398 (August 2007). DOI: 10.1214/105051607000000159


We consider a general model of a heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous character of the model comes from the fact that the monomer units interact with the solvents and with the interface according to some charges that they carry. The charges repeat themselves along the chain in a periodic fashion. The main question concerning this model is whether the polymer remains tightly close to the interface, a phenomenon called localization, or whether there is a marked preference for one of the two solvents, thus yielding a delocalization phenomenon.

In this paper, we present an approach that yields sharp estimates for the partition function of the model in all regimes (localized, delocalized and critical). This, in turn, makes possible a precise pathwise description of the polymer measure, obtaining the full scaling limits of the model. A key point is the closeness of the polymer measure to suitable Markov renewal processes, Markov renewal theory being one of the central mathematical tools of our analysis.


Download Citation

Francesco Caravenna. Giambattista Giacomin. Lorenzo Zambotti. "A renewal theory approach to periodic copolymers with adsorption." Ann. Appl. Probab. 17 (4) 1362 - 1398, August 2007.


Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1136.82391
MathSciNet: MR2344310
Digital Object Identifier: 10.1214/105051607000000159

Primary: 60K35, 82B41, 82B44

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.17 • No. 4 • August 2007
Back to Top