Renormalization Fixed Point of the KPZ Universality Class
Author
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Corwin, Iván
Author
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Quastel, Jeremy
Author
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Remenik Zisis, Daniel
Admission date
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2015-11-03T20:24:15Z
Available date
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2015-11-03T20:24:15Z
Publication date
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2015
Cita de ítem
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Journal of Statistical Physics (2015) 160:815–834
en_US
Identifier
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DOI: 10.1007/s10955-015-1243-8
Identifier
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https://repositorio.uchile.cl/handle/2250/134819
General note
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Artículo de publicación ISI
en_US
Abstract
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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 Airy2
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.