The Strict-Weak Lattice Polymer
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10955_2015_Article_1267.pdf
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Author(s)
Corwin, Ivan
Seppäläinen, Timo
Shen, Hao
Date Issued
May 2015
Journal
Journal of Statistical Physics
Publisher
Springer US
Citation
Corwin, Ivan, Timo Seppäläinen, and Hao Shen. “The Strict-Weak Lattice Polymer.” Journal of Statistical Physics 160.4 (2015): 1027–1053.
Version
Author's final manuscript
Abstract
We introduce the strict-weak polymer model, and show the KPZ universality of the free energy fluctuation of this model for a certain range of parameters. Our proof relies on the observation that the discrete time geometric q-TASEP model, studied earlier by Borodin and Corwin, scales to this polymer model in the limit q→1. This allows us to exploit the exact results for geometric q-TASEP to derive a Fredholm determinant formula for the strict-weak polymer, and in turn perform rigorous asymptotic analysis to show KPZ scaling and GUE Tracy–Widom limit for the free energy fluctuations. We also derive moments formulae for the polymer partition function directly by Bethe ansatz, and identify the limit of the free energy using a stationary version of the polymer model.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10955-015-1267-0
