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

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  • Spohn, Herbert

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.

Suggested Citation

  • Spohn, Herbert, 2006. "Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 71-99.
    • Handle: RePEc:eee:phsmap:v:369:y:2006:i:1:p:71-99
    DOI: 10.1016/j.physa.2006.04.006
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    References listed on IDEAS

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    1. Prähofer, Michael & Spohn, Herbert, 2000. "Statistical self-similarity of one-dimensional growth processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 342-352.
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