Directed Polymers in Random Environment are Diffusive at Weak Disorder

2004/11/10 by Francis Comets, Comets, Francis, Nobuo Yoshida +1 · 1 citation
Mathematics · Physics and Astronomy · #60G42 #82A51 #82D30 #FOS: Mathematics #MSC (2000) 60K35 #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G42 #msc:60K35 #msc:82A51 #msc:82D30

paper · pdf · doi:10.48550/arxiv.math/0411223

openalex publication_date 2004/11/10 · arxiv created 2005/06/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, i.e., where the partition function differs from its annealed value only by a non-vanishing 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.

Cited by

• From disordered systems to the Critical 2D Stochastic Heat Flow

Related

• A short proof of diffusivity for the directed polymers in the weak disorder phase
• Directed polymer in γ-stable Random Environments
• Directed Polymer for very heavy tailed random walks
• The localization transition for the directed polymer in a random environment is smooth
• Strong disorder for a certain class of directed polymers in a random environment