Renormalization Fixed Point of the KPZ Universality Class

@article{Corwin2011RenormalizationFP,
  title={Renormalization Fixed Point of the KPZ Universality Class},
  author={Ivan Corwin and Jeremy Quastel and Daniel Remenik},
  journal={Journal of Statistical Physics},
  year={2011},
  volume={160},
  pages={815-834}
}
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… 
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