Renormalization Fixed Point of the KPZ Universality Class
Author
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 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.
General note
Artículo de publicación ISI
Patrocinador
Fondecyt
1120309
Identifier
URI: https://repositorio.uchile.cl/handle/2250/134819
DOI: DOI: 10.1007/s10955-015-1243-8
Quote Item
Journal of Statistical Physics (2015) 160:815–834
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