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 timeintegrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the large time behavior for the covariance of the height gradients.
 Publication:

SIGMA
 Pub Date:
 July 2016
 DOI:
 10.3842/SIGMA.2016.074
 arXiv:
 arXiv:1602.00486
 Bibcode:
 2016SIGMA..12..074F
 Keywords:

 KPZ universality;
 spacetime correlations;
 interacting particles;
 last passage percolation;
 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Probability
 EPrint:
 SIGMA 12 (2016), 074, 23 pages