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We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by…

Statistical Mechanics · Physics 2009-10-31 H. K. Janssen , U. C. Taeuber , E. Frey

Burgers-Kardar-Parisi-Zhang (KPZ) scaling has recently (re-) surfaced in a variety of physical contexts, ranging from anharmonic chains to quantum systems such as open superfluids, in which a variety of random forces may be encountered…

Statistical Mechanics · Physics 2015-03-24 Philipp Strack

The stochastic PDE known as the Kardar-Parisi-Zhang equation (KPZ) has been proposed as a model for a randomly growing interface. This equation can be reformulated as a stochastic Burgers equation. We study a stochastic KdV-Burgers equation…

Analysis of PDEs · Mathematics 2011-09-23 Geordie Richards

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have…

Statistical Mechanics · Physics 2022-08-31 Enrique Rodriguez-Fernandez , Silvia N. Santalla , Mario Castro , Rodolfo Cuerno

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic dynamical equation yielding non-equilibrium universal scaling. It exhibits notorious non-perturbative aspects. The KPZ fixed point is strong-coupling, all the more…

Statistical Mechanics · Physics 2025-12-11 Léonie Canet

We investigate the scaling regimes of the Kardar-Parisi-Zhang equation in the presence of spatially correlated noise with power law decay $D(p) \sim p^{-2\rho}$ in Fourier space, using a nonperturbative renormalization group approach. We…

Statistical Mechanics · Physics 2014-02-11 Thomas Kloss , Léonie Canet , Bertrand Delamotte , Nicolás Wschebor

In this paper we discuss the well known Kardar Parisi Zhang (KPZ) equation driven by temporally correlated noise. We use a self consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

Kardar-Parisi-Zhang (KPZ) scaling has been observed in discrete polariton lattices, enabled by engineered band structures that stabilize the condensate. Whether this universality extends to intrinsically continuous systems with natural…

Quantum Gases · Physics 2026-04-17 Mikhail Misko , Natalia Starkova , Pavlos G. Lagoudakis

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…

Statistical Mechanics · Physics 2023-12-25 Côme Fontaine , Francesco Vercesi , Marc Brachet , Léonie Canet

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the…

Probability · Mathematics 2019-12-30 Leandro P. R. Pimentel

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic equation featuring non-equilibrium scaling. Although in one dimension, its statistical properties are very well understood, a new scaling regime has been reported…

Statistical Mechanics · Physics 2025-12-04 Liubov Gosteva , Nicolás Wschebor , Léonie Canet

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…

Probability · Mathematics 2022-11-30 Sourav Chatterjee

We investigate space-time coherence in one-dimensional lattices of exciton-polariton condensates formed by fully reconfigurable non-resonant optical pumping. Starting from an open-dissipative Gross-Pitaevskii equation with deterministic…

Mesoscale and Nanoscale Physics · Physics 2025-12-15 D. Novokreschenov , V. Neplokh , M. Misko , N. Starkova , T. Cookson , A. Kudlis , A. Nalitov , I. A. Shelykh , A. V. Kavokin , P. Lagoudakis

In this paper we study the one-dimensional Kardar-Parisi-Zhang equation (KPZ) with correlated noise by field-theoretic dynamic renormalization group techniques (DRG). We focus on spatially correlated noise where the correlations are…

Statistical Mechanics · Physics 2018-06-20 Oliver Niggemann , Haye Hinrichsen

Our understanding of the one-dimensional KPZ equation, \textit{alias} noisy Burgers equation, has advanced substantially over the past five years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice…

Mathematical Physics · Physics 2015-06-24 Jeremy Quastel , Herbert Spohn

We investigate the universal behavior of the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise. The presence of time correlations in the microscopic noise breaks the statistical tilt symmetry, or Galilean invariance, of…

Statistical Mechanics · Physics 2020-01-07 Davide Squizzato , Léonie Canet

Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of…

Probability · Mathematics 2014-06-24 Sergio A. Almada Monter , Amarjit Budhiraja

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is ill-posed because the nonlinearity is marginally defined with respect to the roughness of the forcing noise. However, its Cole-Hopf solution,…

Probability · Mathematics 2014-07-29 Tadahisa Funaki , Jeremy Quastel

We analyze the one-dimensional periodic Kardar-Parisi-Zhang equation in the language of paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer. Apart from deriving a basic existence and uniqueness…

Probability · Mathematics 2016-12-21 Massimiliano Gubinelli , Nicolas Perkowski

We study the KPZ equation with a $1+1-$dimensional spacetime white noise, started at equilibrium, and give a different proof of the main result of \cite{bqs}, i.e., the variance of the solution at time $t$ is of order $t^{2/3}$. Instead of…

Probability · Mathematics 2022-10-27 Yu Gu , Tomasz Komorowski
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