Open Access
Translator Disclaimer
August 1999 A heteropolymer near a linear interface
Marek Biskup, Frank den Hollander
Ann. Appl. Probab. 9(3): 668-687 (August 1999). DOI: 10.1214/aoap/1029962808


We consider a quenched-disordered heteropolymer, consisting of hydrophobic and hydrophylic monomers, in the vicinity of an oil-water interface. The heteropolymer is modeled by a directed simple random walk$(i, S_i)_{i\epsilon\mathbb{N}}$ on $\mathbb{N} \times \mathbb{Z}$ with an interaction given by the Hamiltonians $H_n^{\omega}(S) = \lambda \Sigma_{i=1}^n(\omega_i + h)\text{sign}(S_i)(n \epsilon \mathbb{N})$. Here, $\lambda$ and h are parameters and $(\omega_i)_{i\epsilon\mathbb{N}}$ are i.i.d. $\pm1$-valued random variables. The sign $(S_i) = \pm1$ indicates whether the ith monomer is above or below the interface, the $\omega_i = \pm1$ indicates whether the ith monomer is hydrophobic or hydrophylic. It was shown by Bolthausen and den Hollander that the free energy exhibits a localization-delocalization phase transition at a curve in the $(\lambda, h)$-plane.

In the present paper we show that the free-energy localization concept is equivalent to pathwise localization. In particular, we prove that free-energy localization implies exponential tightness of the polymer excursions away from the interface, strictly positive density of intersections with the interface and convergence of ergodic averages along the polymer. We include an argument due to G. Giacomin, showing that free-energy delocalization implies that there is pathwise delocalization in a certain weak sense.


Download Citation

Marek Biskup. Frank den Hollander. "A heteropolymer near a linear interface." Ann. Appl. Probab. 9 (3) 668 - 687, August 1999.


Published: August 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0971.60098
MathSciNet: MR1722277
Digital Object Identifier: 10.1214/aoap/1029962808

Primary: 60K35
Secondary: 82B44 , 82D30

Keywords: Gibbs state , Heteropolymer , Localization , Quenched disorder

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 3 • August 1999
Back to Top