Renormalization Fixed Point of the KPZ Universality Class
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10955_2015_Article_1243.pdf
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Author(s)
Corwin, Ivan
Quastel, Jeremy
Remenik, Daniel
Date Issued
March 2015
Journal
Journal of Statistical Physics
Publisher
Springer US
Citation
Corwin, Ivan, Jeremy Quastel, and Daniel Remenik. “Renormalization Fixed Point of the KPZ Universality Class.” Journal of Statistical Physics 160.4 (2015): 815–834.
Version
Author's final manuscript
Abstract
The one dimensional Kardar–Parisi–Zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents. These exponents lead to a natural renormalization/rescaling on the space of such evolving interfaces. We introduce and describe the renormalization fixed point of the Kardar–Parisi–Zhang universality class in terms of a random nonlinear semigroup with stationary independent increments, and via a variational formula. Furthermore, we compute a plausible formula the exact transition probabilities using replica Bethe ansatz. The semigroup is constructed from the Airy sheet, a four parameter space-time field which is the Airy[subscript 2] process in each of its two spatial coordinates. Minimizing paths through this field describe the renormalization group fixed point of directed polymers in a random potential. At present, the results we provide do not have mathematically rigorous proofs, and they should at most be considered proposals.
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/s10955-015-1243-8
