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On Time Correlations for KPZ Growth in One Dimension
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 large time behavior for the covariance of the height gradients.
Keywords: KPZ universality, space-time correlations, interacting particles, last passage percolation. 
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     author = {Patrik L. Ferrari and Herbert Spohn},
     title = {On {Time} {Correlations} for {KPZ} {Growth} in {One} {Dimension}},
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}
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Patrik L. Ferrari; Herbert Spohn. On Time Correlations for KPZ Growth in One Dimension. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a73/

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