The Annals of Probability

Directed polymers in random environment are diffusive at weak disorder

Francis Comets and Nobuo Yoshida

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Abstract

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.

Article information

Source
Ann. Probab., Volume 34, Number 5 (2006), 1746-1770.

Dates
First available in Project Euclid: 14 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1163517222

Digital Object Identifier
doi:10.1214/009117905000000828

Mathematical Reviews number (MathSciNet)
MR2271480

Zentralblatt MATH identifier
1104.60061

Subjects
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)

Keywords
Directed polymers random environment weak disorder diffusive behavior invariance principle FKG inequality

Citation

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


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