Directed polymers in random environment are diffusive at weak disorder

By Francis Comets, Nobuo Yoshida. 2004

191 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5451002172377bb3887c29ab41ff5f070dc941ff

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Citations in the corpus

Introduction to KPZ (2011, background): “Later, Comets and Yoshida [CY06] showed that in every dimension there is a critical value βc such that weak disorder holds for 0 ≤ β < βc and strong disorder for β > βc.”
The Kardar-Parisi-Zhang equation and universality class (2011, background): “In d ≥ 3 and weak disorder the walk converges to a Brownian motion, and the limiting diffusion matrix is the same as for standard random walk [45].”
Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, background): “In d ≥ 3 and weak disorder the walk converges to a Brownian motion [22].”
Macdonald processes (2011, background): “In d ≥ 3 and weak disorder the walk converges to a Brownian motion, and the limiting diffusion matrix is the same as for standard random walk [29].”
Scaling for a one-dimensional directed polymer with boundary conditions (2009, background): “In d ≥ 3 and weak disorder the walk converges to a Brownian motion, and the limiting diffusion matrix is the same as for standard random walk [12].”
Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment (2008, background): “Carmona and Hu (2004, [7]), Carmona, Guerra, Hu and Méjane (2006, [5]), Comets, Shiga and Yoshida (2004, [12]), and Comets and Yoshida (2006, [14]).”