One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality.

  title={One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality.},
  author={Tomohiro Sasamoto and Herbert Spohn},
  journal={Physical review letters},
  volume={104 23},
We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for the probability distribution function of the height h(x,t) for all t>0. In particular, we show that for large t, on the scale t(1/3), the statistics is given by the Tracy-Widom distribution, known already from the Gaussian unitary… 

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