相关论文: KPZ equation, its renormalization and invariant me…
We construct explicit jointly invariant measures for the periodic KPZ equation (and therefore also the stochastic Burgers' and stochastic heat equations) for general slope parameters and prove their uniqueness via a one force--one solution…
We study the Kardar-Parisi-Zhang equation on the half-line $x \geqslant 0$ with Neumann type boundary condition. Stationary measures of the KPZ dynamics were characterized in recent work: they depend on two parameters, the boundary…
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 contribution we export these insights to the case…
We construct explicit one-parameter families of stationary measures for the Kardar-Parisi-Zhang equation in half-space with Neumann boundary conditions at the origin, as well as for the log-gamma polymer model in a half-space. The…
This paper deals with the existence and limiting behavior of invariant measures of the stochastic Landau-Lifshitz-Bloch equation driven by linear multiplicative noise and additive noise defined in the entire space $\mathbb{R}^d$ for…
We prove the well-posed character of a regularity structure formulation of the quasilinear generalized (KPZ) equation and give an explicit form for a renormalized equation in the full subcritical regime. Under the assumption that the BPHZ…
We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic…
A recent paper of Tsai shows how the first few moments of a stochastic flow in the space of measures can completely determine its law. Here we give another proof of this result for the particular case of the one-dimensional multiplicative…
The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…
The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1+1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in…
Gaussian Multiplicative Chaos is a way to produce a measure on $\R^d$ (or subdomain of $\R^d$) of the form $e^{\gamma X(x)} dx$, where $X$ is a log-correlated Gaussian field and $\gamma \in [0,\sqrt{2d})$ is a fixed constant. A…
The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we i) pay debts to heroic predecessors, ii) highlight…
We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization group calculation. For a system in which the lattice spacing is smaller than the typical wavelength of the linear instability…
We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…
Consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq 0$. The interface is initially flat, $h(x,t=0)=0$, and driven by a Neumann boundary condition $\partial_x…
We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on…
We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ)…
We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random…
We study the short-time behavior of the probability distribution $\mathcal{P}(H,t)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension. The process starts from a stationary interface: $h(x,t=0)$…
Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…