Influence of spatial correlation for directed polymers

Details Influence of spatial correlation for directed polymers Influence of spatial correlation for directed polymers

2009-12-18

arxiv.org/abs/0912.3732v2

Annals of Probability 2011, Vol. 39, No. 1, 139-175

Mathematics

Probability

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

Scientific paper

10.1214/10-AOP553

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 $d\ge3$ 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.

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