The Kardar-Parisi-Zhang equation - a statistical physics perspective

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.

50 pages, 5 figures, to appear, Les Houches Summer School July 2015 session CIV "Stochastic processes and random matrices", Oxford University Press

Cited by in corpus (6)

• Dynamical phase transition in large deviation statistics of the Kardar-Parisi-Zhang equation
• Short-time height distribution in 1d KPZ equation: starting from a parabola
• Reflected Brownian motions in the KPZ universality class
• Finite-size effects in the short-time height distribution of the Kardar-Parisi-Zhang equation
• Local average height distribution of fluctuating interfaces
• Universal spatio-temporal scaling of distortions in a drifting lattice