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Eigenvalues of GUE Minors

Kurt Johansson, Swedish Royal Institute of Technology (KTH)
Eric Nordenstam, Swedish Royal Institute of Technology (KTH)


Abstract
Consider an infinite random matrix H=(hij)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 μij. We show that the configuration of all these eigenvalues form a determinantal point process. 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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Pages: 1342-1371

Published on: December 20, 2006
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Electronic Journal of Probability. ISSN: 1083-6489