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A diffusive matrix model for invariant $\beta$-ensembles


 
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1. Title Title of document A diffusive matrix model for invariant $\beta$-ensembles
 
2. Creator Author's name, affiliation, country Romain Allez; University Paris Dauphine; France
 
2. Creator Author's name, affiliation, country Alice Guionnet; ÉNS Lyon; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random matrices; stochastic calculus; Interacting particles system; Dyson Brownian motion
 
3. Subject Subject classification 15B52;60B20;60K35;82C22
 
4. Description Abstract We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the orthogonal/unitary group. We also describe the eigenvector dynamics of the limiting matrix process; we show that when $\beta< 1$ and that two eigenvalues collide, the eigenvectors of these two colliding eigenvalues fluctuate very fast and take the uniform measure on the orthocomplement of the eigenvectors of the remaining eigenvalues.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-06-21
 
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/2073
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2073
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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