Takashi Imamura, Tomohiro Sasamoto
Published 2012-10-16Version 1
We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit representation of the probability distribution of the height in terms of the Fredholm determinants. Furthermore from this expression, we also get the exact expression of the space-time two-point correlation function.
Comments: 38 pages, 5 figures
Journal: J. Stat. Phys. 150, 908-939 (2013)
Simple derivation of the $(- λH)^{5/2}$ tail for the 1D KPZ equation
Space of initial conditions and universality in nonequilibrium quantum dynamics
The relaxation of initial condition in systems with infinitely many absorbing states
![QR code for arXiv:1210.4278 [cond-mat.stat-mech]](http://oss.arxitics.com/images/favicon.svg)