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
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.

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Patrik L. Ferrari and Bálint Vető "The hard-edge tacnode process for Brownian motion," Electronic Journal of Probability 22(none), 1-32, (2017). https://doi.org/10.1214/17-EJP97
Received: 25 January 2017; Accepted: 21 August 2017; Published: 2017
Vol.22 • 2017
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