Probability distributions for directed polymers in random media with correlated noise
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PhysRevE.94.010101.pdf
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Author(s)
Chu, Sherry
Kardar, Mehran
Date Issued
July 2016
Journal
Physical Review E
Publisher
American Physical Society
Citation
Chu, Sherry, and Mehran Kardar. “Probability Distributions for Directed Polymers in Random Media with Correlated Noise.” Physical Review E 94.1 (2016): n. pag. © 2016 American Physical Society
Version
Final published version
Abstract
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in d=1+1 dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent β, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.94.010101
