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Related papers: Gaussian fluctuations from the 2D KPZ equation

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In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…

Analysis of PDEs · Mathematics 2023-12-06 Xinyu Cheng

We study a general class of nonlinear Ginzburg-Landau SPDEs in infinite volume under weak nonlinearity scaling and with non-equilibrium initial data. We derive the KPZ equation as a continuum limit of these equations. This makes rigorous…

Probability · Mathematics 2025-12-30 Kevin Yang

We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically…

Statistical Mechanics · Physics 2015-07-24 Xiangyu Cao , Alberto Rosso , Raoul Santachiara

We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of…

Probability · Mathematics 2024-01-01 Ran Tao

A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…

Statistical Mechanics · Physics 2007-05-23 P. J. Forrester

A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the…

Condensed Matter · Physics 2009-10-28 M. Marsili , A. J. Bray

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are…

Statistical Mechanics · Physics 2012-10-29 Patrik L. Ferrari , Alexei Borodin

We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow…

Fluid Dynamics · Physics 2024-03-28 I. V. Kolokolov , V. V. Lebedev , V. M. Parfenyev

In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class…

Analysis of PDEs · Mathematics 2022-08-25 Seokchang Hong , Younghun Hong

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…

Statistical Mechanics · Physics 2023-06-29 Ismael S. S. Carrasco , Tiago J. Oliveira

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations…

Soft Condensed Matter · Physics 2015-06-25 Roland R. Netz , Henri Orland

The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It…

High Energy Physics - Theory · Physics 2015-06-17 Tobias Zingg

The lagrangian of the Kaluza-Klein theory, in its simplest five-dimensional version, should include not only the scalar curvature R, but also the quadratic Gauss-Bonnet invariant. The general lagrangian is computed and the resulting…

Mathematical Physics · Physics 2023-03-21 Richard Kerner

In the present paper, we show that the global solution to (partially) damped Klein-Gordon equation on the three dimensional Euclidean space with small data decays exponentially. The key ingredients in the proof are: Morawetz-type estimates…

Analysis of PDEs · Mathematics 2024-12-10 Yan Cui , Bo Xia

The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…

Analysis of PDEs · Mathematics 2018-10-25 Annalaura Stingo

We prove a reducibility result for a linear Klein-Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving, however we require it to be fast…

Analysis of PDEs · Mathematics 2019-01-25 Luca Franzoi , Alberto Maspero

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

Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone,…

Probability · Mathematics 2021-09-07 Sourav Chatterjee

In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…

Probability · Mathematics 2023-07-04 Raluca M. Balan , Jingyu Huang , Xiong Wang , Panqiu Xia , Wangjun Yuan

We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…

Astrophysics · Physics 2010-10-27 Karim A. Malik