The hard-edge tacnode process for Brownian motion

Ferrari, Patrik and Vető, Bálint (2017) The hard-edge tacnode process for Brownian motion. ELECTRONIC JOURNAL OF PROBABILITY. ISSN 1083-6489

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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.

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