From interacting particle systems to random matrices

Details From interacting particle systems to random matrices From interacting particle systems to random matrices

2010-08-28

arxiv.org/abs/1008.4853v3

J. Stat. Mech. (2010), P10016

Physics

Mathematical Physics

18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.2

Scientific paper

10.1088/1742-5468/2010/10/P10016

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.

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