The Annals of Applied Probability

A heteropolymer in a medium with random droplets

Mario V. Wüthrich

Full-text: Open access


We define a heteropolymer in a medium with random droplets. We prove that for this model we have two regimes: a delocalized one and a localized one. In the localized regime we prove tightness to the droplets, whereas in the delocalized regime we prove diffusive path behavior.

Article information

Ann. Appl. Probab., Volume 16, Number 3 (2006), 1653-1670.

First available in Project Euclid: 2 October 2006

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K99: None of the above, but in this section
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B24: Interface problems; diffusion-limited aggregation 82B26: Phase transitions (general)

Random walk random medium heteropolymer phase transition


Wüthrich, Mario V. A heteropolymer in a medium with random droplets. Ann. Appl. Probab. 16 (2006), no. 3, 1653--1670. doi:10.1214/105051606000000231.

Export citation


  • Albeverio, S. and Zhou, X. Y. (1996). Free energy and some sample path properties of a random walk with random potential. J. Statist. Phys. 83 573–622.
  • Biskup, M. and den Hollander, F. (1999). A heteropolymer near a linear interface. Ann. Appl. Probab. 9 668–687.
  • Bolthausen, E. and den Hollander, F. (1997). Localization transition for a polymer near an interface. Ann. Probab. 25 1334–1366.
  • Garel, T., Huse, D. A., Leibler, S. and Orland, H. (1989). Localization transition of random chains at interfaces. Europhys. Lett. 8 9–13.
  • Grosberg, A., Izrailev, S. and Nechaev, S. (1994). Phase transition in a heteropolymer chain at a selective interface. Phys. Rev. E 50 1912–1921.
  • den Hollander, F. and Wüthrich, M. V. (2004). Diffusion of a heteropolymer in a multi-interface medium. J. Statist. Phys. 114 849–889.
  • den Hollander, F. and Whittington, S. G. (2005). Localization transition for a copolymer in an emulsion. Preprint.
  • Kingman, J. F. C. (1973). Subadditive ergodic theorem. Ann. Probab. 1 883–909.
  • Maritan, A., Riva, M. P. and Trovato, A. (1999). Heteropolymers in a solvent at an interface. J. Phys. A Math. Gen. 32 L275–L280.
  • Martin, R., Causo, M. S. and Whittington, S. G. (2000). Localization transition for a randomly coloured self-avoiding walk at an interface. J. Phys. A Math. Gen. 33 7903–7918.
  • Orlandini, E., Rechnitzer, A. and Whittington, S. G. (2002). Random copolymers and the Morita approximation: Polymer adsorption and polymer localization. J. Phys. A 35 7729–7751.
  • Sinai, Ya. G. (1993). A random walk with random potential. Theory Probab. Appl. 38 382–385.
  • Sinai, Ya. G. (1995). A remark concerning random walks with random potentials. Fund. Math. 147 173–180.