相关论文: Universality of KPZ equation

The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the…

For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…

We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic $3:2:1$ scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that when the…

We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…

We use the notion of energy solutions of the stochastic Burgers equation to give a short proof of the Hairer-Quastel universality result for a class of stationary weakly asymmetric stochastic PDEs.

We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…

In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…

The logarithm of the diagonal matrix element of a high power of a random matrix converges to the Cole-Hopf solution of the Kardar-Parisi-Zhang equation in the sense of one-point distributions.

We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average…

We study the one-dimensional KPZ equation on a large torus, started at equilibrium. The main results are optimal variance bounds in the super-relaxation regime and part of the relaxation regime.

We derive an exact generalization of the well-known Lebowitz--Percus--Verlet (LPV) formula that relates the kinetic energy fluctuations of an isolated system to its specific heat. Our general formula, obtained by the application of…

We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small…

What is the probability that all the gas in a box accumulates in the same half of this box? Though amusing, this question underlies the fundamental problem of density fluctuations at equilibrium, which has profound implementations in many…

We consider some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion process. For these models, in the limit of large time t, universality of…

We study the aging property for stationary models in the KPZ universality class. In particular, we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary KPZ equation, the height function of the stationary…

Adopting the Landau-Lifshiftz method of classical fluctuations we determine the statistical average strength of the fluctuations of the energy flux on the apparent horizon of a homogeneous and isotropic universe described by Einstein…

In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli [5] and…

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs with the corresponding distribution for…

We study the continuity of weak solutions for quasilinear elliptic systems with source terms of critical growth arising from a transport-energy structure. The latter occurs frequently in connection with the first balance principles of…

In the present paper, we study the equilibrium fluctuations of a particle system in infinite volume with two conserved quantities and long-range dependence. More specifically, the model of interest is the so-called ABC model, in which three…