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Certain polymer models are known to exhibit path localization in the sense that at low temperatures, the average fractional overlap of two independent samples from the Gibbs measure is bounded away from $0$.
Absence of diffusion in certain random lattices
Anderson, P. W · 1958
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Pinning and roughening of domain walls in Ising systems due to random impurities
Huse, D. A., and Henley, C. L · 1985
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Some rigorous results on the Sherrington-Kirkpatrick spin glass model
Aizenman, M., Lebowitz, J. L., and Ruelle, D · 1987
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Diffusion of directed polymers in a random environment
Imbrie, J. Z., and Spencer, T · 1988
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The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case
Comets, F., and Neveu, J · 1995
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On the partition function of a directed polymer in a Gaussian random environment
Carmona, P., and Hu, Y · 2002
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Directed polymer for very heavy tailed random walks
Viveros, R · 2003
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Directed polymers in random environment are diffusive at weak disorder
Comets, F., and Yoshida, N · 2006
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Parisi measures
Talagrand, M · 2006
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Random polymers
den Hollander, F · 2007
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Strong localization and macroscopic atoms for directed polymers
Vargas, V · 2007
Cited alongside, same era.
On differentiability of the Parisi formula
Panchenko, D · 2008
Cited alongside, same era.
Directed polymers in a random environment with heavy tails
Auffinger, A., and Louidor, O · 2011
Cited alongside, same era.
Scaling for a one-dimensional directed polymer with boundary conditions
Seppäläinen, T · 2012
Cited alongside, same era.
Overlaps and pathwise localization in the Anderson polymer model
Comets, F., and Cranston, M · 2013
Cited alongside, same era.
Localization transition for polymers in Poissonian medium
Comets, F., and Yoshida, N · 2013
Cited alongside, same era.
The lebesgue measure of zero set of a polynomial function is zero
(https://math.stackexchange.com/users/822/nate eldredge), N. E · 2016
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Pinning model with heavy tailed disorder
Torri, N · 2016
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Localization of directed polymers with general reference walk
Bates, E · 2018
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Directed polymers in heavy-tail random environment
Berger, Q., and Torri, N · 2019
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Proof of the Path Localization Conjecture for Directed Polymers
Chatterjee, S · 2019
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Localization of directed polymers in continuous space
Bakhtin, Y., and Seo, D · 2020
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Directed polymers in random environments
Comets, F · 2016
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Localization in log-gamma polymers with boundaries
Comets, F., and Nguyen, V.-L · 2016
Cited alongside, same era.
High temperature limits for ( 1 + 1 ) (1+1) -dimensional directed polymer with heavy-tailed disorder
Dey, P. S., and Zygouras, N · 2016
Cited alongside, same era.
Brownian polymers in Poissonian environment: a survey
Comets, F., and Cosco, C
Cited in the paper.
Bates, E., and Chatterjee, S · 2020
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Localization in Gaussian disordered systems at low temperature
Bates, E., and Chatterjee, S · 2020
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The Scaling Limit of the Directed Polymer with Power-Law Tail Disorder
Berger, Q., and Lacoin, H · 2021
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