Universality of KPZ equation

Abstract

We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states are given by energy solutions of the KPZ equation. As a consequence, we prove that the Cole-Hofp solutions are also energy solutions of the KPZ equation.

35 pages

References in corpus (5)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Nonequilibrium Central Limit Theorem for a Tagged Particle in Symmetric Simple Exclusion
• $t^{1/3}$ Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on $\mathbb{Z}$
• Scaling exponent for the Hopf-Cole solution of KPZ/Stochastic Burgers

Cited by in corpus (19)

• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• A stochastic Burgers equation from a class of microscopic interactions
• Phase transition in equilibrium fluctuations of symmetric slowed exclusion
• Crossover to the KPZ equation
• Singular stochastic PDEs
• Energy solutions of KPZ are unique
• Some recent progress in singular stochastic PDEs
• Lectures on singular stochastic PDEs
• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
• Diffusivity of lattice gases
• A rigorous equation for the Cole-Hopf solution of the conservative KPZ equation
• Regularization by noise and stochastic Burgers equations
• Comments on David Aldous and Persi Diaconis' "Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem"
• Probabilistic approach to the stochastic Burgers equation
• A resolvent-type method for estimating time integrals of quadratic fluctuations in weakly asymmetric exclusion
• Scalings limits for the exclusion process with a slow site
• Scaling limits of additive functionals of interacting particle systems
• Renormalized-Generalized Solutions for the KPZ Equation
• Strong solution of the stochastic Burgers equation