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January 2011 Influence of spatial correlation for directed polymers
Hubert Lacoin
Ann. Probab. 39(1): 139-175 (January 2011). DOI: 10.1214/10-AOP553

Abstract

In this paper, we study a model of a Brownian polymer in ℝ+×ℝd, 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≥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.

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Hubert Lacoin. "Influence of spatial correlation for directed polymers." Ann. Probab. 39 (1) 139 - 175, January 2011. https://doi.org/10.1214/10-AOP553

Information

Published: January 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1208.82084
MathSciNet: MR2778799
Digital Object Identifier: 10.1214/10-AOP553

Subjects:
Primary: 60K35 , 60K37 , 82D60

Keywords: coarse graining , Directed polymer , fractional moment estimates , Free energy , Quenched disorder , Strong disorder , Superdiffusivity

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 1 • January 2011
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