Communications in Mathematical Physics

, Volume 209, Issue 2, pp 437-476

First online:

Shape Fluctuations and Random Matrices

  • Kurt JohanssonAffiliated withDepartment of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden.¶

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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).