ECP Reading Tools

Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble
2.	Creator	Author's name, affiliation, country	Pascal Bianchi; Télécom Paristech
2.	Creator	Author's name, affiliation, country	Mérouane Debbah; Alcatel-Lucent chair on flexible radio, SUPELEC
2.	Creator	Author's name, affiliation, country	Jamal Najim; CNRS and Télécom Paristech
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random matrix; eigenvalues; asymptotic independence; Gaussian unitary ensemble
3.	Subject	Subject classification	15B52;15A18;60F05
4.	Description	Abstract	Consider a $n \times n$ matrix from the Gaussian Unitary Ensemble (GUE). Given a finite collection of bounded disjoint real Borel sets $(\Delta_{i,n},\ 1\leq i\leq p)$ with positive distance from one another, eventually included in any neighbourhood of the support of Wigner's semi-circle law and properly rescaled (with respective lengths $n^{-1}$ in the bulk and $n^{-2/3}$ around the edges), we prove that the related counting measures ${\mathcal N}_n(\Delta_{i,n}), (1\leq i\leq p)$, where ${\mathcal N}_n(\Delta)$ represents the number of eigenvalues within $\Delta$, are asymptotically independent as the size $n$ goes to infinity, $p$ being fixed. As a consequence, we prove that the largest and smallest eigenvalues, properly centered and rescaled, are asymptotically independent; we finally describe the fluctuations of the ratio of the extreme eigenvalues of a matrix from the GUE.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Agence Nationale de la Recherche; programme
7.	Date	(YYYY-MM-DD)	2010-09-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1568
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1568
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.