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Eigenvalues of GUE Minors


 
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1. Title Title of document Eigenvalues of GUE Minors
 
2. Creator Author's name, affiliation, country Kurt Johansson; Swedish Royal Institute of Technology (KTH)
 
2. Creator Author's name, affiliation, country Eric Nordenstam; Swedish Royal Institute of Technology (KTH)
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrices; Tiling problems;
 
3. Subject Subject classification 60G55; 15A52; 52C20
 
4. Description 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.

 
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Göran Gustafsson Foundation (KVA)
 
7. Date (YYYY-MM-DD) 2006-12-20
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/370
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-370
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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