On Time Correlations for KPZ Growth in One Dimension

  title={On Time Correlations for KPZ Growth in One Dimension},
  author={Patrik L. Ferrari and Herbert Spohn},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  • P. Ferrari, H. Spohn
  • Published 1 February 2016
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
Time correlations for KPZ growth in 1 + 1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance… 

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