Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions.

@article{Calabrese2011ExactSF,
  title={Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions.},
  author={Pasquale Calabrese and Pierre Le Doussal},
  journal={Physical review letters},
  year={2011},
  volume={106 25},
  pages={
          250603
        }
}
We provide the first exact calculation of the height distribution at arbitrary time t of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer with one end fixed, one free, and the Bethe ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of… 

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