The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 17, Number 4 (2007), 1362-1398.
A renewal theory approach to periodic copolymers with adsorption
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.
Ann. Appl. Probab. Volume 17, Number 4 (2007), 1362-1398.
First available in Project Euclid: 10 August 2007
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
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