On Time Correlations for KPZ Growth in One Dimension

Symmetry Integrability and Geometry-Methods and Applications

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