Symmetry Integrability and Geometry-Methods and Applications | |
On Time Correlations for KPZ Growth in One Dimension | |
article | |
Patrik L. Ferrari1  Herbert Spohn2  | |
[1] Institute for Applied Mathematics, Bonn University;Zentrum Mathematik, TU München | |
关键词: KPZ universality; space-time correlations; interacting particles; last passage percolation; | |
DOI : 10.3842/SIGMA.2016.074 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300001107ZK.pdf | 624KB | download |