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Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals

Herbert Spohn
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Abstract

Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.

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Herbert Spohn. 2005-12-01. Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals. https://doi.org/10.1016/j.physa.2006.04.006

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