# Stationary Correlations for the 1D KPZ Equation

@article{Imamura2013StationaryCF, title={Stationary Correlations for the 1D KPZ Equation}, author={Takashi Imamura and Tomohiro Sasamoto}, journal={Journal of Statistical Physics}, year={2013}, volume={150}, pages={908-939} }

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…

## 76 Citations

Integration by Parts and the KPZ Two-Point Function

- Mathematics
- 2020

In this article we consider the KPZ fixed point starting from a two-sided Brownian motion with an arbitrary diffusion coefficient. We apply the integration by parts formula from Malliavin calculus to…

Large deviations for the KPZ equation from the KP equation

- Mathematics
- 2019

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…

Height Fluctuations for the Stationary KPZ Equation

- Mathematics
- 2014

We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X)$\mathcal {H}(0,X)=B(X)$, for B(X) a two-sided standard Brownian motion) and show that…

Half-space stationary Kardar–Parisi–Zhang equation beyond the Brownian case

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

We study the Kardar–Parisi–Zhang (KPZ) equation on the half-line x ⩾ 0 with Neumann type boundary condition. Stationary measures of the KPZ dynamics were characterized in recent work: they depend on…

Coupled Kardar-Parisi-Zhang Equations in One Dimension

- Physics, Mathematics
- 2013

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…

Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions

- Mathematics
- 2017

For stationary interface growth, governed by the Kardar–Parisi–Zhang (KPZ) equation in 1+1 dimensions, typical fluctuations of the interface height at long times are described by the Baik–Rains…

Replica analysis of the one-dimensional KPZ equation

- Physics
- 2014

In the last few years several exact solutions have been obtained for the onedimensional KPZ equation, which describes the dynamics of growing interfaces. In particular the computations based on…

KP governs random growth off a 1-dimensional substrate

- Mathematics, PhysicsForum of Mathematics, Pi
- 2022

Abstract The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation.…

Simple derivation of the (– λ H)5/2 tail for the 1D KPZ equation

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2018

We study the long-time regime of the Kardar–Parisi–Zhang (KPZ) equation in 1 + 1 dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large…

Reflected Brownian Motions in the KPZ Universality Class

- Mathematics
- 2016

A system of asymmetrically reflected Brownian motions is studied under various initial conditions. Asymmetric reflection means that each particle is reflected from its left neighbor. This system can…

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