On Time Correlations for KPZ Growth in One Dimension
Abstract
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 with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the l arge time behavior for the covariance of the height gradients.
Cite
@article{arxiv.1602.00486,
title = {On Time Correlations for KPZ Growth in One Dimension},
author = {Patrik L. Ferrari and Herbert Spohn},
journal= {arXiv preprint arXiv:1602.00486},
year = {2016}
}