The Annals of Probability
- Ann. Probab.
- Volume 34, Number 5 (2006), 1746-1770.
Directed polymers in random environment are diffusive at weak disorder
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.
Ann. Probab., Volume 34, Number 5 (2006), 1746-1770.
First available in Project Euclid: 14 November 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60G42: Martingales with discrete parameter 82A51 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
Comets, Francis; Yoshida, Nobuo. Directed polymers in random environment are diffusive at weak disorder. Ann. Probab. 34 (2006), no. 5, 1746--1770. doi:10.1214/009117905000000828. https://projecteuclid.org/euclid.aop/1163517222