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2006 Eigenvalues of GUE Minors
Kurt Johansson, Eric Nordenstam
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Electron. J. Probab. 11: 1342-1371 (2006). DOI: 10.1214/EJP.v11-370


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 $(i,\mu_j^i)$ 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.

An Erratum to this paper has been published in Electronic Journal of Probability, Volume 12 (2007), paper number 37.



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Kurt Johansson. Eric Nordenstam. "Eigenvalues of GUE Minors." Electron. J. Probab. 11 1342 - 1371, 2006.


Accepted: 20 December 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1127.60047
MathSciNet: MR2268547
Digital Object Identifier: 10.1214/EJP.v11-370

Primary: 60G55
Secondary: 15A52 , 52C20

Keywords: random matrices , Tiling problems

Vol.11 • 2006
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