Electronic Journal of Probability

The hard-edge tacnode process for Brownian motion

Patrik L. Ferrari and Bálint Vető

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 79, 32 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1506931229

Digital Object Identifier
doi:10.1214/17-EJP97

Mathematical Reviews number (MathSciNet)
MR3710799

Zentralblatt MATH identifier
1380.60013

Subjects
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)

Keywords
non-colliding walks determinantal processes tacnode process edge scaling limit

Rights
Creative Commons Attribution 4.0 International License.

Citation

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


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