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

Herbert Spohn

Physica A: Statistical Mechanics and its Applications, 2006, vol. 369, issue 1, 71-99

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.

Keywords: Determinantal processes; Edge scaling; Matrix-valued Brownian motion (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:369:y:2006:i:1:p:71-99

DOI: 10.1016/j.physa.2006.04.006

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