Electronic Journal of Probability

Eigenvalues of GUE Minors

Kurt Johansson and Eric Nordenstam

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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.


Article information

Electron. J. Probab., Volume 11 (2006), paper no. 50, 1342-1371.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 15A52 52C20: Tilings in $2$ dimensions [See also 05B45, 51M20]

Random matrices Tiling problems

This work is licensed under aCreative Commons Attribution 3.0 License.


Johansson, Kurt; Nordenstam, Eric. Eigenvalues of GUE Minors. Electron. J. Probab. 11 (2006), paper no. 50, 1342--1371. doi:10.1214/EJP.v11-370. https://projecteuclid.org/euclid.ejp/1464730585

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