Lacoin, Hubert Superdiffusivity for directed polymer in correlated random environment. (Superdiffusivity for directed polymer in corelated random environment.) (English) Zbl 1480.60052 Actes Rencontres C.I.R.M. 2, No. 1, 25-26 (2010). Summary: 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 superdiffusivity also occurs in higher dimensions. MSC: 60F05 Central limit and other weak theorems 82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) 60G50 Sums of independent random variables; random walks Keywords:random environment; random walk; superdiffusivity × Cite Format Result Cite Review PDF Full Text: DOI References: [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. | · 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. · 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 . | · Zbl 1042.60069 [5] F. Comets and V. Vargas \(Majorizing multiplicative cascades for directed polymers in random media\), ALEA 2 (2006), 267-277. · 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 . | · 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. [8] J.Z. Imbrie and T. Spencer, \(Diffusion of Directed Polymers in a Random Environment\), Jour. Stat. Phys. 52 (1988), 609-622. · Zbl 1084.82595 [9] H. Lacoin, \(New bounds for the free energy of directed polymers in dimension \)1 + 1\( and \)1 + 2\[, Commun. Math. Phys. 294 (2010) 471-50\] · Zbl 1227.82098 [10] H. Lacoin \(Influence of spacial correlation for directed polymers\), to appear in Ann. Probab. · Zbl 1208.82084 [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. | · Zbl 1041.60079 [12] M. Petermann, \(Superdiffusivity of directed polymers in random environment\), Phd Thesis (2000). Copyright Cellule MathDoc 2018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.