Open Access
2017 The hard-edge tacnode process for Brownian motion
Patrik L. Ferrari, Bálint Vető
Electron. J. Probab. 22: 1-32 (2017). DOI: 10.1214/17-EJP97


We consider $N$ non-intersecting Brownian bridges conditioned to stay below a fixed threshold. We consider a scaling limit where the limit shape is tangential to the threshold. In the large $N$ limit, we determine the limiting distribution of the top Brownian bridge conditioned to stay below a function as well as the limiting correlation kernel of the system. It is a one-parameter family of processes which depends on the tuning of the threshold position on the natural fluctuation scale. We also discuss the relation to the six-vertex model and to the Aztec diamond on restricted domains.


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Patrik L. Ferrari. Bálint Vető. "The hard-edge tacnode process for Brownian motion." Electron. J. Probab. 22 1 - 32, 2017.


Received: 25 January 2017; Accepted: 21 August 2017; Published: 2017
First available in Project Euclid: 2 October 2017

zbMATH: 1380.60013
MathSciNet: MR3710799
Digital Object Identifier: 10.1214/17-EJP97

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

Keywords: Determinantal processes , edge scaling limit , Non-colliding walks , Tacnode process

Vol.22 • 2017
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