Eigenvalues of GUE Minors

Kurt Johansson, Eric Nordenstam
2006 Electronic Journal of Probability  
Consider an infinite random matrix H = (h ij ) 0<i,j picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by H i = (hrs) 1≤r,s≤i and let the j:th largest eigenvalue of H i 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
more » ... nding limit for random lozenge tilings of a hexagon. This version of this article differs from the one published in Electronic Journal of Probability in that the errors listed in the separate erratum have been corrected.
doi:10.1214/ejp.v11-370 fatcat:hgx5pb3lffcnnhgeqrafjcnkq4