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Non-colliding Brownian bridges and the asymmetric tacnode process


 
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1. Title Title of document Non-colliding Brownian bridges and the asymmetric tacnode process
 
2. Creator Author's name, affiliation, country Patrik Lino Ferrari; Bonn University; Germany
 
2. Creator Author's name, affiliation, country Bálint Vető; Bonn University; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Non-colliding walks; determinantal processes; tacnode; limit processes; universality
 
3. Subject Subject classification 60B20; 60G55; 60J65; 60J10
 
4. Description Abstract We consider non-colliding Brownian bridges starting from two points and returning to the same position. These positions are chosen such that, in the limit of large number of bridges, the two families of bridges just touch each other forming a tacnode. We obtain the limiting process at the tacnode, the "asymmetric tacnode process". It is a determinantal point process with correlation kernel given by two parameters: (1) the curvature's ratio $\lambda>0$ of the limit shapes of the two families of bridges, (2) a parameter $\sigma$ controlling the interaction on the fluctuation scale. This generalizes the result for the symmetric tacnode process ($\lambda=1$ case).
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported by the Hausdorff Center for Mathematics and the German Research Foundation via the SFB611-A12 project. The work of B.V. was partially supported by OTKA (Hungarian National Research Fund) grant K100473.
 
7. Date (YYYY-MM-DD) 2012-06-14
 
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/1811
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1811
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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