Stationary Correlations for the 1D KPZ Equation

  title={Stationary Correlations for the 1D KPZ Equation},
  author={Takashi Imamura and Tomohiro Sasamoto},
  journal={Journal of Statistical Physics},
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… 
Integration by Parts and the KPZ Two-Point Function
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Recently, Quastel and Remenik \cite{QRKP} [arXiv:1908.10353] found a remarkable relation between some solutions of the finite time Kardar-Parisi-Zhang (KPZ) equation and the Kadomtsev-Petviashvili
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Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our
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Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions.
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Fluctuation exponent of the KPZ/stochastic Burgers equation
(1.4) hε(t, x) = ε 1/2h(ε−zt, ε−1x). We will be considering these models in equilibrium, in which case h(t, x)−h(t, 0) is a two-sided Brownian motion with variance ν−1σ2 for each t. There are many
Numerical evidence for stretched exponential relaxations in the Kardar-Parisi-Zhang equation.
  • E. Katzav, M. Schwartz
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
This work presents results from extensive numerical integration of the Kardar-Parisi-Zhang equation in 1+1 dimensions aimed to check the long-time behavior of the dynamical structure factor of the KPZ system and gives an analytic expression that yields a very good approximation to the numerical data.
The one-dimensional KPZ equation and the Airy process
Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a