Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 79, 32 pp.
The hard-edge tacnode process for Brownian motion
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.
Electron. J. Probab., Volume 22 (2017), paper no. 79, 32 pp.
Received: 25 January 2017
Accepted: 21 August 2017
First available in Project Euclid: 2 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 60G55: Point processes
Secondary: 60J65: Brownian motion [See also 58J65] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Ferrari, Patrik L.; Vető, Bálint. The hard-edge tacnode process for Brownian motion. Electron. J. Probab. 22 (2017), paper no. 79, 32 pp. doi:10.1214/17-EJP97. https://projecteuclid.org/euclid.ejp/1506931229