Electronic Journal of Probability, Volume 12 (2007), paper number 37</a>.">
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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