## The Annals of Applied Probability

### A renewal theory approach to periodic copolymers with adsorption

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 17, Number 4 (2007), 1362-1398.

Dates
First available in Project Euclid: 10 August 2007

https://projecteuclid.org/euclid.aoap/1186755243

Digital Object Identifier
doi:10.1214/105051607000000159

Mathematical Reviews number (MathSciNet)
MR2344310

Zentralblatt MATH identifier
1136.82391

#### Citation

Caravenna, Francesco; Giacomin, Giambattista; Zambotti, Lorenzo. A renewal theory approach to periodic copolymers with adsorption. Ann. Appl. Probab. 17 (2007), no. 4, 1362--1398. doi:10.1214/105051607000000159. https://projecteuclid.org/euclid.aoap/1186755243

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