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The transition from a weak-disorder (diffusive phase) to a strong-disorder (localized phase) for directed polymers in a random environment is a well studied phenomenon.
D. A. Huse, C. L. Henley Pinning and roughening of domain walls in ising systems due to random impurities
1985
Earlier work this paper cites.
J.Z. Imbrie, T. Spencer Diffusion of directed polymer in a random environment
1988
Earlier work this paper cites.
E. Bolthausen, A Note on the Diffusion of Directed Polymers in a Random Environment
1989
Earlier work this paper cites.
S. Albeverio, X. Zhou A martingale approach to directed polymers in a random environment
1996
Earlier work this paper cites.
R. Song, X. Zhou A Remark on Diffusion of Directed Polymers in Random Environments
1996
Earlier work this paper cites.
F. Comets, T. Shiga, N. Yoshida Directed polymers in a random environment: path localization and strong disorder
2003
Earlier work this paper cites.
F. Comets, T. Shiga, and N. Yoshida. Probabilistic analysis of directed polymers in a random environment: a review
2004
Cited alongside, same era.
F. Comets, N. Yoshida Directed Polymers in Random Environment are Diffusive at Weak Disorder
2006
Cited alongside, same era.
F. Comets Weak disorder for low dimensional polymers: The model of stable laws
2006
Cited alongside, same era.
B. Derrida, G. Giacomin, H. Lacoin, F. Toninelli Fractional Moment Bounds and Disorder Relevance for Pinning Models
2009
Cited alongside, same era.
F. Toninelli Coarse graining, fractional moments and the critical slope of random copolymers
2009
Cited alongside, same era.
H. Lacoin New Bounds for the Free Energy of Directed Polymers in Dimension 1 + 1 and 1 + 2
H. Lacoin, Influence of spatial correlation for directed polymers
2011
Later among the works it cites.
F. Watbled Sharp asymptotics for the free energy of 1 + 1 1+1 dimensional directed polymers in an infinitely divisible environment
2012
Later among the works it cites.
K. Alexander, G Yldrm Directed polymers in a random environment with a defect line
2015
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F. Comets Directed Polymers in Random Environments
2016
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Q. Berger, H. Lacoin The High-Temperature Behavior For The Directed Polymer In Dimension 1 + 2
2017
Later among the works it cites.
H. Lacoin, J. Sohier (2016) Disorder relevance without Harris Criterion: the case of pinning model with γ \gamma -stable environment
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2010
Cited alongside, same era.
H. Lacoin Marginal relevance for the γ \gamma -stable pinning model
Cited in the paper.
M. Nakashimi Free energy of directed polymer in random environment in 1 + 1 1+1 -dimension at high temperature
Cited in the paper.
2017
Later among the works it cites.