Universality of KPZ equation
Patricia Goncalves, Milton Jara
TL;DR
This paper introduces energy solutions for the KPZ equation and demonstrates their universality by connecting particle system fluctuations and Cole-Hopf solutions, establishing a broad framework for understanding KPZ universality.
Contribution
It defines energy solutions for the KPZ equation and proves their universality across different models and solutions, including Cole-Hopf solutions.
Findings
Density fluctuations are described by energy solutions of KPZ.
Cole-Hopf solutions are also energy solutions of KPZ.
Universality of KPZ equation in particle systems established.
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.
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Taxonomy
TopicsRandom Matrices and Applications · Theoretical and Computational Physics · Stochastic processes and statistical mechanics