On time correlations for KPZ growth in one dimension

Patrik L. Ferrari, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

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 large time behavior for the covariance of the height gradients.

Original languageEnglish
Article number074
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume12
DOIs
StatePublished - 26 Jul 2016

Keywords

  • Interacting particles
  • KPZ universality
  • Last passage percolation
  • Space-time correlations

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