Abstract
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 Schrödinger equation. The notes are an extended version of my lectures at Les Houches July 2015.
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