Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 15(2010) > Paper 38 open journal systems 


The Martingale approach to disorder irrelevance for pinning models

Hubert Lacoin, Università di Roma Tre


Abstract
This paper presents a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent alpha in (0,1/2). We also give a new upper bound for the contact fraction of the disordered model at criticality.


Full text: PDF

Pages: 418-427

Published on: September 30, 2010


Bibliography
  1. Alexander, Kenneth S. The effect of disorder on polymer depinning transitions. Comm. Math. Phys. 279 (2008), no. 1, 117--146. MR2377630 (2008m:82045)
  2. Alexander, Kenneth S.; Zygouras, Nikos. Quenched and annealed critical points in polymer pinning models. Comm. Math. Phys. 291 (2009), no. 3, 659--689. MR2534789 (2010h:60271)
  3. Alexander, Kenneth S.; Zygouras, Nikos. Equality of critical points for polymer depinning transitions with loop exponent one. Ann. Appl. Probab. 20 (2010), no. 1, 356--366. MR2582651
  4. N. H. Bingham, C. M. Goldie and J. L. Teugels. Regular variation, Cambridge University Press, Cambridge, 1987.
  5. Bolthausen, Erwin. A note on the diffusion of directed polymers in a random environment. Comm. Math. Phys. 123 (1989), no. 4, 529--534. MR1006293 (91a:60270)
  6. Comets, Francis; Yoshida, Nobuo. Directed polymers in random environment are diffusive at weak disorder. Ann. Probab. 34 (2006), no. 5, 1746--1770. MR2271480 (2007m:60305)
  7. Doney, R. A. One-sided local large deviation and renewal theorems in the case of infinite mean. Probab. Theory Related Fields 107 (1997), no. 4, 451--465. MR1440141 (98e:60040)
  8. Derrida, Bernard; Giacomin, Giambattista; Lacoin, Hubert; Toninelli, Fabio Lucio. Fractional moment bounds and disorder relevance for pinning models. Comm. Math. Phys. 287 (2009), no. 3, 867--887. MR2486665 (2010a:82029)
  9. Derrida, B.; Hakim, V.; Vannimenus, J. Effect of disorder on two-dimensional wetting. J. Statist. Phys. 66 (1992), no. 5-6, 1189--1213. MR1156401 (93e:82022)
  10. Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403 (42 #5292)
  11. Fisher, Michael E. Walks, walls, wetting, and melting. J. Statist. Phys. 34 (1984), no. 5-6, 667--729. MR0751710 (85j:82022)
  12. G. Forgacs, J. M. Luck, Th. M. Nieuwenhuizen and H. Orland, Wetting of a disordered substrate: exact critical behavior in two dimensions, Phys. Rev. Lett. 57 (1986), 2184--2187.
  13. Giacomin, Giambattista. Random polymer models.Imperial College Press, London, 2007. xvi+242 pp. ISBN: 978-1-86094-786-5; 1-86094-786-7 MR2380992 (2009c:82025)
  14. Giacomin, Giambattista; Lacoin, Hubert; Toninelli, Fabio. Marginal relevance of disorder for pinning models. Comm. Pure Appl. Math. 63 (2010), no. 2, 233--265. MR2588461
  15. Giacomin, Giambattista; Toninelli, Fabio Lucio. Smoothing effect of quenched disorder on polymer depinning transitions. Comm. Math. Phys. 266 (2006), no. 1, 1--16. MR2231963 (2007d:82029)
  16. Harris A.B, Effect of Random Defects on the Critical Behaviour of Ising Models, J. Phys. C 7 (1974) 1671--1692.
  17. H. Lacoin, Hierarchical pinning model with site disorder: Disorder is marginally relevant, Probab. Theory Relat. Fields 148 (2010) 159--175.
  18. Toninelli, Fabio Lucio. Critical properties and finite-size estimates for the depinning transition of directed random polymers. J. Stat. Phys. 126 (2007), no. 4-5, 1025--1044. MR2311896 (2008c:82044)
  19. Toninelli, Fabio Lucio. A replica-coupling approach to disordered pinning models. Comm. Math. Phys. 280 (2008), no. 2, 389--401. MR2395475 (2009b:82059)
  20. Walters, Peter. An introduction to ergodic theory.Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. ix+250 pp. ISBN: 0-387-90599-5 MR0648108 (84e:28017)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X