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Eigenvalues of GUE minors. (English) Zbl 1127.60047
Summary: Consider an infinite random matrix \(H=(h_{ij})_{0<i,j}\) picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by \(H_i=(h_{rs})_{1\leq r,s\leq i}\) and let the \(j\)-th largest eigenvalue of \(H_i\) be \(\mu ^{i}_{j}\). We show that the configuration of all these eigenvalues form a determinantal point process on \(\mathbb N \times \mathbb R\).
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.

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
15B52 Random matrices (algebraic aspects)
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
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