Electronic Journal of Probability

Eigenvalues of GUE Minors

Kurt Johansson and Eric Nordenstam

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464730585

Digital Object Identifier
doi:10.1214/EJP.v11-370

Mathematical Reviews number (MathSciNet)
MR2268547

Zentralblatt MATH identifier
1127.60047

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

Keywords
Random matrices Tiling problems

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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