Related papers: A central limit theorem for the KPZ equation
We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards-Wilkinson equation with an effective variance.
We consider a borderline case: the central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the iid case a well-known sufficient condition for this central limit theorem is regular…
This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…
In this paper, we present a quantitative central limit theorem for the d-dimensional stochastic heat equation driven by a Gaussian multiplicative noise, which is white in time and has a spatial covariance given by the Riesz kernel. We show…
In this paper, we study the spatial averages of the solution to the parabolic Anderson model driven by a space-time Gaussian homogeneous noise that is colored in time and space. We establish quantitative central limit theorems (CLT) of this…
We study the continuum space-time limit of a periodic one dimensional array of deterministic logistic maps coupled diffusively. First, we analyse this system in connection with a stochastic one dimensional Kardar-Parisi-Zhang (KPZ) equation…
We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
We study the dynamics and unbinding transition of vortices in the compact anisotropic Kardar-Parisi-Zhang (KPZ) equation. The combination of non-equilibrium conditions and strong spatial anisotropy drastically affects the structure of…
In this contribution, we are interested in the analysis of a semi-implicit time discretization scheme for the approximation of a parabolic equation driven by multiplicative colored noise involving a $p$-Laplace operator (with $p\geq 2$),…
We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an…
We consider the asymptotic behavior of the KPZ fixed point $\{\mathsf H(x,t)\}_{x\in\mathbb R, t>0}$ conditioned on $\mathsf H(0,T)=L$ as $L$ goes to infinity. The main result is a conditional limit theorem for the fluctuations of $\mathsf…
We prove the height functions for a class of non-integrable and non-stationary particle systems converge to the KPZ equation, thereby making progress on the universality of the KPZ equation. The models herein are ASEP [4] with a mesoscopic…
We prove existence and uniqueness of distributional solutions to the KPZ equation globally in space and time, with techniques from paracontrolled analysis. Our main tool for extending the analysis on the torus to the full space is a…
We study the fixed-time spatial covariance of the KPZ equation with flat initial profile. Using Malliavin calculus and a Clark-Ocone representation, we show that as $|x|\to\infty$, $\mathrm{Cov}[h(t,x),h(t,0)]$ is governed by a…
We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory…
We consider the periodic totally asymmetric simple exclusion process with a general initial condition that properly approximates a periodic upper-semicontinuous function. We find the large time limit of the rescaled space-time multipoint…
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,…
The focus of this work is the numerical approximation of time-dependent partial differential equations associated to initial-boundary value problems. This master dissertation is mostly concerned with the actual computation of the solution…
We examine in greater detail the proposal that time is the conjugate of the constants of nature. Fundamentally distinct times are associated with different constants, a situation often found in "relational time" settings. We show in detail…