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Phys Rev Lett. 2000 May 22;84(21):4882-5.

Universal distributions for growth processes in 1+1 dimensions and random matrices

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Zentrum Mathematik and Physik Department, TU Munchen, D-80290 Munchen, Germany.


We develop a scaling theory for Kardar-Parisi-Zhang growth in one dimension by a detailed study of the polynuclear growth model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential.

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