Directed polymers in random environment are diffusive at weak disorder

Comets, Francis; Yoshida, Nobuo

Ann. Probab., Tome 34 (2006) no. 1, p. 1746-1770 / Harvested from Project Euclid

Résumé

In this paper we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, that is, where the partition function differs from its annealed value only by a nonvanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove monotonicity of the phase diagram in the temperature.

Publié le : 2006-09-14
Classification: Directed polymers, random environment, weak disorder, diffusive behavior, invariance principle, FKG inequality, 60K35, 60G42, 82A51, 82D30

@article{1163517222,
     author = {Comets, Francis and Yoshida, Nobuo},
     title = {Directed polymers in random environment are diffusive at weak disorder},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 1746-1770},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163517222}
}

Comets, Francis; Yoshida, Nobuo. Directed polymers in random environment are diffusive at weak disorder. Ann. Probab., Tome 34 (2006) no. 1, pp.  1746-1770. http://gdmltest.u-ga.fr/item/1163517222/