Eigenvalues of GUE minors
نویسندگان
چکیده
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 μ i j . We show that the configuration of all these eigenvalues (i, μ i j) form a determinantal point process on N × R. 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.
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