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2012 Non-colliding Brownian bridges and the asymmetric tacnode process
Patrik Ferrari, Bálint Vető
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Electron. J. Probab. 17: 1-17 (2012). DOI: 10.1214/EJP.v17-1811


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).


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Patrik Ferrari. Bálint Vető. "Non-colliding Brownian bridges and the asymmetric tacnode process." Electron. J. Probab. 17 1 - 17, 2012.


Accepted: 14 June 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1258.60011
MathSciNet: MR2946151
Digital Object Identifier: 10.1214/EJP.v17-1811

Primary: 60B20
Secondary: 60G55 , 60J10 , 60J65

Keywords: Determinantal processes , limit processes , Non-colliding walks , tacnode , Universality


Vol.17 • 2012
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