Indexing metadata

Convergence of the eigenvalue density for Laguerre beta ensembles on short scales


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Convergence of the eigenvalue density for Laguerre beta ensembles on short scales
 
2. Creator Author's name, affiliation, country Philippe Sosoe; Princeton University; United States
 
2. Creator Author's name, affiliation, country Percy Wong; D.E. Shaw & Co.; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Ranbom Matrices, Beta Ensembles, Marchenko-Pastur law
 
3. Subject Subject classification 60B20
 
4. Description Abstract In this note, we prove that the normalized trace of the resolvent of the beta-Laguerre ensemble eigenvalues is close to the Stieltjes transform of the Marchenko-Pastur (MP) distribution with very high probability, for values of the imaginary part greater than $m^{1+\varepsilon}$. As an immediate corollary, we obtain convergence of the one-point density to the MP law on short scales. The proof serves to illustrate some simplifications of the method introduced in our previous work to prove a local semi-circle law for Gaussian beta-ensembles.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSERC, NSF
 
7. Date (YYYY-MM-DD) 2014-03-15
 
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/2638
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2638
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en 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.