An expert review of the KPZ equation's history, mathematical developments, and applications, with no new research results.
The Kardar-Parisi-Zhang equation - a statistical physics perspective
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The article covers the one-dimensional Kardar-Parisi-Zhang equation, weak drive limit, universality, directed polymers in a random medium, replica solutions, statistical mechanics of line ensembles, and its generalization to several components which is used to study equilibrium time correlations of anharmonic chains and of the discrete nonlinear Schr\"{o}dinger equation. The notes are an extended version of my lectures at Les Houches July 2015.
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Dynamic scaling of growing interfaces
An expert review of the KPZ equation's history, mathematical developments, and applications, with no new research results.