, Volume 209, Issue 2, pp 437-476

Shape Fluctuations and Random Matrices

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Abstract:

We study a certain random growth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy–Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE).

Received: 12 March 1999 / Accepted: 19 August 1999