Abstract
A simple martingale argument is presented which proves that directed polymers in random environments satisfy a central limit theorem ford≧3 and if the disorder is small enough. This simplifies and extends an approach by J. Imbrie and T. Spencer.
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References
Imbrie, J.Z., Spencer, T.: Diffusions of directed polymers in a random environment. J. Stat. Phys.52, 609 (1988)
Neveu, J.: Discrete parameter martingales. Amsterdam: North-Holland 1975
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Communicated by J. Fröhlich
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Bolthausen, E. A note on the diffusion of directed polymers in a random environment. Commun.Math. Phys. 123, 529–534 (1989). https://doi.org/10.1007/BF01218584
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DOI: https://doi.org/10.1007/BF01218584