Coarse graining, fractional moments and the critical slope of random copolymers

Fabio Lucio Toninelli (CNRS and ENS Lyon)

Abstract


For a much-studied model of random copolymer at a selective interface we prove that the slope of the critical curve in the weak-disorder limit is strictly smaller than 1, which is the value given by the annealed inequality. The proof is based on a coarse-graining procedure, combined with upper bounds on the fractional moments of the partition function.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 531-547

Publication Date: February 23, 2009

DOI: 10.1214/EJP.v14-612

References

  1. K. S. Alexander and N. Zygouras. Quenched and annealed critical points in polymer pinning models. arXiv:0805.1708. Math. Review number not available.
  2. T. Bodineau and G. Giacomin. On the localization transition of random copolymers near selective interfaces J. Statist. Phys. 117 (2004), 801--818. MR2107896 (2005g:82057)
  3. T. Bodineau, G. Giacomin, H. Lacoin and F. L. Toninelli. Copolymers at selective interfaces: new bounds on the phase diagram. J. Statist. Phys. 132 (2008), 603-626. MR2429695
  4. E. Bolthausen, F. Caravenna and B. de Tilière. The quenched critical point of a diluted disordered polymer model. Stochastic Process. Appl., to appear. arXiv:0711.0141v1 [math.PR]. Math. Review number not available.
  5. E. Bolthausen and F. den Hollander. Localization transition for a polymer near an interface. Ann. Probab. 25 (1997), 1334--1366. MR1457622 (98h:60149)
  6. F. Caravenna, G. Giacomin and M. Gubinelli. A Numerical Approach to Copolymers at Selective Interfaces. J. Statist. Phys. 122 (2006), 799--832. MR2213950 (2006k:82049)
  7. B. Derrida, G. Giacomin, H. Lacoin and F. L. Toninelli. Fractional moment bounds and disorder relevance for pinning models. Commun. Math. Phys., to appear. arXiv:0712.2515 [math.PR]. Math. Review number not available.
  8. R. A. Doney. One-sided local large deviations and renewal theorems in the case of infinite mean. Probab. Theory Rel. Fields 107 (1997), 451--465. MR1440141 (98e:60040)
  9. W. Feller. An introduction to probability theory and its applications, Vol. I, Second Edition, John Wiley & Sons, 1966. MR0228020 (37 #3604)
  10. T. Garel, D. A. Huse, S. Leibler and H. Orland. Localization transition of random chains at interfaces. Europhys. Lett. 8 (1989), 9--13. Math. Review number not available.
  11. G. Giacomin. Random Polymer Models. Imperial College Press, London (2007). MR2380992
  12. G. Giacomin, H. Lacoin and F. L. Toninelli. Hierarchical pinning models, quadratic maps and quenched disorder. Probab. Theory Rel. Fields, to appear. arXiv:0711.4649 [math.PR]. Math. Review number not available.
  13. G. Giacomin and F. L. Toninelli. Estimates on path delocalization for copolymers at selective interfaces. Probab.Theory Rel. Fields 133 (2005), 464--482. MR2197110 (2006m:60137)
  14. C. Monthus. On the localization of random heteropolymers at the interface between two selective solvents. Eur. Phys. Journal B 13 (2000), 111--130. Math. Review number not available.
  15. F. L. Toninelli. Disordered pinning models and copolymers: beyond annealed bounds. Ann. Appl. Probab. 18 (2008), 1569-1587. MR2434181
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.