# Superdiffusivity for directed polymer in corelated random environment

Hubert Lacoin^{[1]}

- [1] Università degli Studi “Roma Tre”, Largo San Leonardo Murialdo, 00146 Roma

Actes des rencontres du CIRM (2010)

- Volume: 2, Issue: 1, page 25-26
- ISSN: 2105-0597

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topLacoin, Hubert. "Superdiffusivity for directed polymer in corelated random environment." Actes des rencontres du CIRM 2.1 (2010): 25-26. <http://eudml.org/doc/115845>.

@article{Lacoin2010,

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.},

affiliation = {Università degli Studi “Roma Tre”, Largo San Leonardo Murialdo, 00146 Roma},

author = {Lacoin, Hubert},

journal = {Actes des rencontres du CIRM},

language = {eng},

month = {12},

number = {1},

pages = {25-26},

publisher = {CIRM},

title = {Superdiffusivity for directed polymer in corelated random environment},

url = {http://eudml.org/doc/115845},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Lacoin, Hubert

TI - Superdiffusivity for directed polymer in corelated random environment

JO - Actes des rencontres du CIRM

DA - 2010/12//

PB - CIRM

VL - 2

IS - 1

SP - 25

EP - 26

AB - 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.

LA - eng

UR - http://eudml.org/doc/115845

ER -

## References

top- Anderson, P. W. (1958). Absence of Diffusion in Certain Random Lattices, Phys. Rev. 109, 1492–1505.
- E. Bolthausen, A note on diffusion of directed polymeres in a random environment, Commun. Math. Phys. 123 (1989), 529–534. Zbl0684.60013MR1006293
- 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. Zbl1015.60100MR1939654
- F. Comets ,T. Shiga and N. Yoshida, Directed Polymers in a random environment: strong disorder and path localization, Bernoulli 9 4 (2003), 705–723 . Zbl1042.60069MR1996276
- F. Comets and V. Vargas Majorizing multiplicative cascades for directed polymers in random media, ALEA 2 (2006), 267–277. Zbl1105.60074MR2249671
- F. Comets and N. Yoshida Directed polymers in a random environment are diffusive at weak disorder, Ann. Probab. 34 (2006), 1746–1770 . Zbl1104.60061MR2271480
- 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. MR789757
- J.Z. Imbrie and T. Spencer, Diffusion of Directed Polymers in a Random Environment, Jour. Stat. Phys. 52 (1988), 609–622. Zbl1084.82595MR968950
- 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. Zbl1227.82098MR2579463
- H. Lacoin Influence of spacial correlation for directed polymers, to appear in Ann. Probab.
- 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. Zbl1041.60079MR2060455
- M. Petermann, Superdiffusivity of directed polymers in random environment, Phd Thesis (2000).

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