Universality of KPZ equation
classification
🧮 math.PR
cond-mat.stat-mechmath-phmath.APmath.MP
keywords
equationsolutionsenergyproveassumptionsasymmetriccole-hofpconsequence
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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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