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From the Pearcey to the Airy Process.


 
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1. Title Title of document From the Pearcey to the Airy Process.
 
2. Creator Author's name, affiliation, country Mark Adler; Brandeis University; United States
 
2. Creator Author's name, affiliation, country Mattia Cafasso; Université de Montréal; Canada
 
2. Creator Author's name, affiliation, country Pierre van Moerbeke; Université Catholique de Louvain; Belgium
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Airy process; Pearcey process; Dyson's Brownian motions.
 
3. Subject Subject classification 60K35; 60B20.
 
4. Description Abstract Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's dynamics, then leads to interesting, infinite-dimensional diffusions for the eigenvalues. This paper studies the relationship between two of the models, namely the Airy and Pearcey processes and more precisely shows how to approximate the multi-time statistics for the Pearcey process by the one of the Airy process with the help of a PDE governing the gap probabilities for the Pearcey process.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF, ESF, Nato, FNRS, Francqui Foundation.
 
7. Date (YYYY-MM-DD) 2011-06-01
 
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/898
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-898
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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