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.

Caravenna, F., Giacomin, G., Zambotti, L. (2007). A renewal theory approach to periodic copolymers with adsorption. THE ANNALS OF APPLIED PROBABILITY, 17(4), 1362-1398 [10.1214/105051607000000159].

A renewal theory approach to periodic copolymers with adsorption

CARAVENNA, FRANCESCO;
2007

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.
Articolo in rivista - Articolo scientifico
Random walks, renewal theory, Markov renewal theory, scaling limits, polymer models, wetting models
English
2007
17
4
1362
1398
none
Caravenna, F., Giacomin, G., Zambotti, L. (2007). A renewal theory approach to periodic copolymers with adsorption. THE ANNALS OF APPLIED PROBABILITY, 17(4), 1362-1398 [10.1214/105051607000000159].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/21114
Citazioni
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 11
Social impact