Centre de diffusion de revues académiques mathématiques

  
 
 
 

Actes des rencontres du CIRM

Table des matières de ce fascicule | Article précédent | Article suivant
Hubert Lacoin
Superdiffusivity for directed polymer in corelated random environment
Actes des rencontres du CIRM, 2 no. 1: Déviations pour les temps locaux d’auto-intersections (2010), p. 25-26, doi: 10.5802/acirm.19
Article PDF

Résumé - Abstract

The directed polymer in random environment models the behavior of a polymer chain in a solution with impurities. It is a particular case of random walk in random environment. In $1+1$ dimensional environment is has been shown by Petermann that this random walk is superdiffusive. We show superdiffusivity properties are reinforced were there are long ranged correlation in the environment and that super diffusivity also occurs in higher dimensions.

Bibliographie

[1] Anderson, P. W. (1958). Absence of Diffusion in Certain Random Lattices, Phys. Rev. 109, 1492–1505.
[2] E. Bolthausen, A note on diffusion of directed polymeres in a random environment, Commun. Math. Phys. 123 (1989), 529–534.
Article |  MR 1006293 |  Zbl 0684.60013
[3] P. Carmona and Y. Hu, On the partition function of a directed polymer in a random Gaussian environment , Probab. Theor. Relat. Fields 124 3 (2002), 431–457.  MR 1939654 |  Zbl 1015.60100
[4] F. Comets ,T. Shiga and N. Yoshida, Directed Polymers in a random environment: strong disorder and path localization, Bernoulli 9 4 (2003), 705–723 .
Article |  MR 1996276 |  Zbl 1042.60069
[5] F. Comets and V. Vargas Majorizing multiplicative cascades for directed polymers in random media, ALEA 2 (2006), 267–277.  MR 2249671 |  Zbl 1105.60074
[6] F. Comets and N. Yoshida Directed polymers in a random environment are diffusive at weak disorder, Ann. Probab. 34 (2006), 1746–1770 .
Article |  MR 2271480 |  Zbl 1104.60061
[7] C.L. Henley and D.A. Huse, Pinning and roughening of domain wall in Ising systems due to random impurities, Phys. Rev. Lett. 54 (1985) 2708–2711.  MR 789757
[8] J.Z. Imbrie and T. Spencer, Diffusion of Directed Polymers in a Random Environment, Jour. Stat. Phys. 52 (1988), 609–622.  MR 968950 |  Zbl 1084.82595
[9] H. Lacoin, New bounds for the free energy of directed polymers in dimension $1+1$ and $1+2$, Commun. Math. Phys. 294 (2010) 471-503.  MR 2579463
[10] H. Lacoin Influence of spacial correlation for directed polymers, to appear in Ann. Probab.
Article
[11] O. Méjane Upper bound of a volume exponent for directed polymers in a random environment Ann. Inst. H. Poincaré Probab. Stat. 40 (2004), 299–308.
Numdam |  MR 2060455 |  Zbl 1041.60079
[12] M. Petermann, Superdiffusivity of directed polymers in random environment, Phd Thesis (2000).
Copyright Cellule MathDoc 2013 | Crédit | Plan du site