Open Access
September 2006 Directed polymers in random environment are diffusive at weak disorder
Francis Comets, Nobuo Yoshida
Ann. Probab. 34(5): 1746-1770 (September 2006). DOI: 10.1214/009117905000000828


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.


Download Citation

Francis Comets. Nobuo Yoshida. "Directed polymers in random environment are diffusive at weak disorder." Ann. Probab. 34 (5) 1746 - 1770, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1104.60061
MathSciNet: MR2271480
Digital Object Identifier: 10.1214/009117905000000828

Primary: 60K35
Secondary: 60G42 , 82A51 , 82D30

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

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 5 • September 2006
Back to Top