Consider an infinite random matrix H=(hᵢⱼ)0 < i,j picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by Hᵢ=(hᵣₛ)1≤ r,s≤ i and let the j:th largest eigenvalue of Hᵢ be μⁱⱼ. We show that the configuration of all these eigenvalues (i,μⱼⁱ) form a determinantal point process on N. Furthermore we show that this process can be obtained as the scaling limit in random tilings of the Aztec diamond close to the boundary. We also discuss the corresponding limit for random lozenge tilings of a hexagon. An Erratum to this paper has been published in Electronic Journal of Probability, Volume 12 (2007), paper number 37.
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Johansson et al. (2006) studied this question.
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