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From sine kernel to Poisson statistics


 
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1. Title Title of document From sine kernel to Poisson statistics
 
2. Creator Author's name, affiliation, country Romain Allez; Weierstrass Institute; Germany
 
2. Creator Author's name, affiliation, country Laure Dumaz; University of Cambridge; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrices, Diffusions, Poisson point process, Exit time problem
 
3. Subject Subject classification 60G55 ; 60G17 ; 60B20 ; 60J60
 
4. Description Abstract We study the Sine beta process introduced in Valko and Virag, when the inverse temperature beta tends to 0. This point process has been shown to be the scaling limit of the eigenvalues point process in the bulk of beta-ensembles and its law is characterised in terms of the winding numbers of the Brownian carrousel at different angular speeds. After a careful analysis of this family of coupled diffusion processes, we prove that the Sine-beta point process converges weakly to a Poisson point process on the real line. Thus, the Sine-beta point processes establish a smooth crossover between the rigid clock (or picket fence) process (corresponding to $\beta=\infty$) and the Poisson process.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2014-12-12
 
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/3742
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3742
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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