Mathematics – Probability
Scientific paper
2005-07-08
Annals of Applied Probability 2007, Vol. 17, No. 4, 1362-1398
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/105051607000000159 the Annals of Applied Probability (http://www.imstat.org/aap/) by
Scientific paper
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.
Caravenna Francesco
Giacomin Giambattista
Zambotti Lorenzo
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