Influence of spatial correlation for directed polymers

Abstract

In this paper, we study a model of a Brownian polymer in ${\mathbb{R}}_{+}\times {\mathbb{R}}^d$, introduced by Rovira and Tindel [J. Funct. Anal. 222 (2005) 178--201]. Our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy, fluctuation exponent and volume exponent. In particular, we prove that under some assumptions, very strong disorder and superdiffusivity hold at all temperatures when $d\ge 3$ and provide a novel approach to Petermann's superdiffusivity result in dimension one [Superdiffusivity of directed polymers in random environment (2000) Ph.D. thesis]. We also derive results for a Brownian model of pinning in a nonrandom potential with power-law decay at infinity.

Published in at http://dx.doi.org/10.1214/10-AOP553 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• A replica-coupling approach to disordered pinning models
• Scaling exponent for the Hopf-Cole solution of KPZ/Stochastic Burgers
• Superdiffusivity for a Brownian polymer in a continuous Gaussian environment

Cited by in corpus (7)

• Localization Transition for Polymers in Poissonian Medium
• Localization of directed polymers with general reference walk
• On the Long-range Directed Polymer Model
• A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimension
• From Directed Polymers in Spatial-correlated Environment to Stochastic Heat Equations Driven by Fractional Noise in 1 + 1 Dimensions
• Superdiffusivity for Brownian motion in a Poissonian potential with long range correlation II: upper bound on the volume exponent
• Superdiffusivity for Brownian Motion in a Poissonian Potential with Long Range Correlation I: Lower Bound on the Volume Exponent